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FALLING SHADOWS APPLIED TO SUBALGEBRAS AND IDEALS OF BCK/BCI-ALGEBRAS

Young-Bae Jun, Chul-Hwan Park
<span title="2012-06-25">2012</span> <i title="The Homan Mathematical Society"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xyretfalcvbtvbigm3jfiejxh4" style="color: black;">Honam Mathematical Journal</a> </i> &nbsp;
falling subalgebra/ideal of a BCK/BCI-algebra is introduced. Relations between falling subalgebras and falling ideals are given.  ...  Relations between fuzzy subalgebras/ideals and falling subalgebras/ideals are provided. A characterization of a falling ideal is established.  ...  [5, 6] established a theoretical approach to define a fuzzy inference relation and fuzzy set operations based on the theory of falling shadows.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5831/hmj.2012.34.2.135">doi:10.5831/hmj.2012.34.2.135</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b5zy3hczzneb7fm7kw2nks7dly">fatcat:b5zy3hczzneb7fm7kw2nks7dly</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170826050814/http://ocean.kisti.re.kr/downfile/volume/hmsk/HNSHCY/2012/v34n2/HNSHCY_2012_v34n2_135.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/04/9c/049c3b72e522bc8678516f290d24f21db18d0f44.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5831/hmj.2012.34.2.135"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Virtual shadow modules and their link invariants [article]

Jackson Blankstein and Susan Kim and Catherine Lepel and Sam Nelson and Nicole Sanderson
<span title="2012-04-18">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We introduce an algebra Z[X,S] associated to a pair (X,S) of a virtual birack X and X-shadow S.  ...  We use modules over Z[X,S] to define enhancements of the virtual birack shadow counting invariant, extending the birack shadow module invariants to virtual case.  ...  Definition 10 Let X be a set with virtual birack structure B(x, y) = (y x , x y ) and V (x, y) = (y x , x y ) and let S be an X-shadow.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1110.1778v2">arXiv:1110.1778v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6ubatxdx7veyxpsdldzvhtms24">fatcat:6ubatxdx7veyxpsdldzvhtms24</a> </span>
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Falling -Ideals in -Algebras

Young Bae Jun, Sun Shin Ahn, Kyoung Ja Lee
<span title="">2011</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3s4wom7forhp3klujcroiocrpi" style="color: black;">Discrete Dynamics in Nature and Society</a> </i> &nbsp;
Based on the theory of a falling shadow which was first formulated by Wang (1985), a theoretical approach of the ideal structure in -algebras is established.  ...  A relation between a fuzzy -subalgebra and a falling -subalgebra is provided.  ...  They investigated several relations between d-algebras and BCK-algebras as well as several other relations between d-algebras and oriented digraphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2011/516418">doi:10.1155/2011/516418</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v6im2k2mgjh4fia6n6lndfi4xa">fatcat:v6im2k2mgjh4fia6n6lndfi4xa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200209085124/http://downloads.hindawi.com/journals/ddns/2011/516418.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/77/2d/772deb356393bc3eb9821737d86e50dcc5c3ad7c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2011/516418"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> hindawi.com </button> </a>

Page 5333 of Mathematical Reviews Vol. , Issue 98H [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
While scalar QES equations are related to the usual Lie algebras, QES systems of coupled equations are related to graded algebras, in general, not of Lie type.  ...  Another prospec- tive direction for investigation is a relation between the concrete structures of the quasi-exactly solvable Hamiltonians and the ge- ometry of the manifolds they define through the corresponding  ... 
<span class="external-identifiers"> </span>
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The Theory of Falling Shadows Applied to -Ideals in -Algebras

Young Bae Jun, Sun Shin Ahn
<span title="">2012</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/umoxruxnnfe4pmrmuxws6l5gue" style="color: black;">International Journal of Mathematics and Mathematical Sciences</a> </i> &nbsp;
On the basis of the theory of a falling shadow which was first formulated by Wang (1985), the notion of falling -ideals in -algebras is introduced, and related properties are investigated.  ...  Relations among falling -ideals, falling -ideals, falling -ideals, falling -subalgebras, and fallingBCK-ideals are discussed.  ...  They investigated several relations between d-algebras and BCK-algebras as well as several other relations between d-algebras and oriented digraphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2012/693090">doi:10.1155/2012/693090</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nzd2evsbtvg3zjh2aozvegyafi">fatcat:nzd2evsbtvg3zjh2aozvegyafi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190223191843/http://pdfs.semanticscholar.org/4bf2/b0663f744d5497c9f4971e4dc44d6735937f.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4b/f2/4bf2b0663f744d5497c9f4971e4dc44d6735937f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2012/693090"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> hindawi.com </button> </a>

Falling fuzzy quasi-associative ideals of BCI-algebras

Young Jun, Seok Song
<span title="">2012</span> <i title="National Library of Serbia"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5h57vchldreh5kwnkzol2rss4m" style="color: black;">Filomat</a> </i> &nbsp;
As a generalization of a fuzzy quasi-associative ideal of a BCI-algebra, the notion of a falling fuzzy quasi-associative ideal of a BCI-algebra is introduced by using the theory of a falling shadow.  ...  Relations between falling fuzzy ideals and falling fuzzy quasi-associative ideals are given. Conditions for a falling fuzzy ideal to be a falling fuzzy quasi-associative ideal are provided.  ...  Based on these results, we will apply the theory of falling shadows to the related algebraic structures, for example, MV-algebras, MTL-algebras, R 0 -algebras and BL-algebras, etc., in the future study  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2298/fil1204649j">doi:10.2298/fil1204649j</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jesu34sph5a33fbeyzw3iqchum">fatcat:jesu34sph5a33fbeyzw3iqchum</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809003833/http://www.pmf.ni.ac.rs/pmf/publikacije/filomat/2012/F26-4-2012/F26-4-2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/18/b4/18b4e510f8e08f6cac04f58d5734907c1292b8d5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2298/fil1204649j"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Fuzzy positive implicative ideals of BCK-algebras based on the theory of falling shadows

Young Bae Jun, Min Su Kang
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nkrwe4pmozafvnd72yxufztpku" style="color: black;">Computers and Mathematics with Applications</a> </i> &nbsp;
On the basis of the theory of a falling shadow, the notion of a falling fuzzy positive implicative ideal of a BCK-algebra is introduced.  ...  Relations between falling fuzzy positive implicative ideals and falling fuzzy ideals are given.  ...  Wang and Sanchez [2] introduced the theory of falling shadows which directly relates probability concepts to the membership function of fuzzy sets.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.camwa.2010.10.029">doi:10.1016/j.camwa.2010.10.029</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cnicrq246fdbpd6hzetxdhw2we">fatcat:cnicrq246fdbpd6hzetxdhw2we</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170929070222/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/75c/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDg5ODEyMjExMDAwODE5OQ%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/dd/15/dd15a44e331e36ec47b2ff04f23eeb5215271f80.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.camwa.2010.10.029"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

CHARACTERIZATIONS OF FALLING FUZZY IDEALS

Young-Bae Jun, Seok-Zun Song, Eun-Hwan Roh
<span title="2012-03-25">2012</span> <i title="The Homan Mathematical Society"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xyretfalcvbtvbigm3jfiejxh4" style="color: black;">Honam Mathematical Journal</a> </i> &nbsp;
Characterizations of falling fuzzy positive implicative ideals and other related ideals are discussed.  ...  Relations among falling fuzzy ideals, falling fuzzy implicative ideals, falling fuzzy positive implicative ideals and falling fuzzy commutative ideals are considered.  ...  Wang and Sanchez [14] introduced the theory of falling shadows which directly relates probability concepts with the membership function of fuzzy sets.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5831/hmj.2012.34.1.125">doi:10.5831/hmj.2012.34.1.125</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pzgsr6apo5hzpbxty24zq6more">fatcat:pzgsr6apo5hzpbxty24zq6more</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170822230341/http://ocean.kisti.re.kr/downfile/volume/hmsk/HNSHCY/2012/v34n1/HNSHCY_2012_v34n1_125.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c8/e5/c8e552c7c7aed1eb12179983505902b317177f80.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5831/hmj.2012.34.1.125"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Implicative Ideals of BCK-Algebras Based on the Fuzzy Sets and the Theory of Falling Shadows

Young Bae Jun, Min Su Kang, Chul Hwan Park
<span title="">2010</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/umoxruxnnfe4pmrmuxws6l5gue" style="color: black;">International Journal of Mathematics and Mathematical Sciences</a> </i> &nbsp;
Based on the theory of falling shadows and fuzzy sets, the notion of a falling fuzzy implicative ideal of a BCK-algebra is introduced.  ...  Relations between fuzzy implicative ideals and falling fuzzy implicative ideals are provided.  ...  Wang and Sanchez 2 introduced the theory of falling shadows which directly relates probability concepts with the membership function of fuzzy sets.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2010/819463">doi:10.1155/2010/819463</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/npf6zfldovepxc44qmzwteoplq">fatcat:npf6zfldovepxc44qmzwteoplq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808012904/http://emis.math.tifr.res.in/journals/HOA/IJMMS/Volume2010/819463.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6d/f3/6df34b1964036f4975db90bf7ca2d4b5fdf61f28.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2010/819463"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> hindawi.com </button> </a>

FALLING FUZZY BCI-COMMUTATIVE IDEALS

Young Bae Jun, Seok-Zun Song
<span title="2014-09-25">2014</span> <i title="The Homan Mathematical Society"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xyretfalcvbtvbigm3jfiejxh4" style="color: black;">Honam Mathematical Journal</a> </i> &nbsp;
On the basis of the theory of a falling shadow and fuzzy sets, the notion of a falling fuzzy BCI-commutative ideal of a BCI-algebra is introduced.  ...  Relations between falling fuzzy BCI-commutative ideals and falling fuzzy ideals are given. Relations between fuzzy BCI-commutative ideals and falling fuzzy BCIcommutative ideals are provided.  ...  Wang and Sanchez [2] introduced the theory of falling shadows which directly relates probability concepts with the membership function of fuzzy sets.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5831/hmj.2014.36.3.555">doi:10.5831/hmj.2014.36.3.555</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lrqwbdhsxnewxnlliizodxn74m">fatcat:lrqwbdhsxnewxnlliizodxn74m</a> </span>
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Intuitionistic Falling Shadow Theory with Applications in BCK/BCI-Algebras

Young Jun, Seok-Zun Song, Kyoung Lee
<span title="2018-08-13">2018</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ye33srllvnanjouxn4tmrfgjsq" style="color: black;">Mathematics</a> </i> &nbsp;
Intuitionistic falling shadow is introduced, and applied to B C K / B C I -algebras.  ...  Falling intuitionistic subalgebra and falling intuitionistic ideal of B C K / B C I -algebras are introduced, and related properties are investigated.  ...  [5, 6] established a theoretical approach to define a fuzzy inference relation and fuzzy set operations based on the theory of falling shadows.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/math6080138">doi:10.3390/math6080138</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/p7f4ldjczfbgnhmfzo6b72sy5i">fatcat:p7f4ldjczfbgnhmfzo6b72sy5i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190505225957/https://res.mdpi.com/mathematics/mathematics-06-00138/article_deploy/mathematics-06-00138.pdf?filename=&amp;attachment=1" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7d/20/7d20533e4904410ca17f01ee2f9927d56843fc0d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/math6080138"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a>

Graph model of the Heisenberg–Weyl algebra

P Blasiak, A Horzela, G H E Duchamp, K A Penson, A I Solomon
<span title="2010-03-01">2010</span> <i title="IOP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wxgp7pobnrfetfizidmpebi4qy" style="color: black;">Journal of Physics, Conference Series</a> </i> &nbsp;
We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure.  ...  This provides a deeper insight into the algebraic structure of Quantum Theory and sheds light on the intrinsic combinatorial underpinning of its abstract formalism.  ...  Again, similarly as g and g 1 in diag. (3) , both algebras are related by G ∼ A A G 1 ⊃ h h (10) Hence, the algebra G 1 is the shadow of the more structured algebra of graphs G.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/1742-6596/213/1/012014">doi:10.1088/1742-6596/213/1/012014</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/anl2ifq245fgzg3rx2vxzpss54">fatcat:anl2ifq245fgzg3rx2vxzpss54</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200823021036/https://arxiv.org/pdf/0710.0266v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2f/1b/2f1bf3b18d00f4819a9c731f7be97e014922f22d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/1742-6596/213/1/012014"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> iop.org </button> </a>

Birack shadow modules and their link invariants [article]

Sam Nelson, Katie Pelland
<span title="2011-06-01">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We introduce an associative algebra Z[X,S] associated to a birack shadow and define enhancements of the birack counting invariant for classical knots and links via representations of Z[X,S] known as shadow  ...  We provide examples which demonstrate that the shadow module enhanced invariants are not determined by the Alexander polynomial or the unenhanced birack counting invariants.  ...  The Shadow Algebra and Shadow Modules In [1] an associative algebra is defined with generators corresponding to ordered pairs of elements of a finite quandle X, with relations obtained from Reidemeister  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1106.0336v1">arXiv:1106.0336v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/33wgoydkf5cord46yx4qhafqfa">fatcat:33wgoydkf5cord46yx4qhafqfa</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1106.0336/1106.0336.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1106.0336v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Mini-Workshop: Rank One Groups and Exceptional Algebraic Groups

Tom De Medts, Bernhard Mühlherr, Anastasia Stavrova
<span title="2020-11-18">2020</span> <i title="European Mathematical Society - EMS - Publishing House GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mnv35em3uvgxdkcbx2cvykhugu" style="color: black;">Oberwolfach Reports</a> </i> &nbsp;
The most interesting examples arise from exceptional algebraic groups of relative rank one. This class of groups is, in turn, intimately related to structurable algebras.  ...  The goal of the mini-workshop was to bring together experts on these topics in order to make progress towards a better understanding of the structure of rank one groups.  ...  As noted before, structurable algebras and Lie algebras are also closely related.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4171/owr/2019/52">doi:10.4171/owr/2019/52</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2zo742tsmve4ppougkbdan5ehm">fatcat:2zo742tsmve4ppougkbdan5ehm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210428204640/https://biblio.ugent.be/publication/8686300/file/8686305" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b1/c4/b1c4dac0e5f9f6365af988e75a0baed194944339.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4171/owr/2019/52"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Positive implicative ideals of BCK-algebras based on neutrosophic sets and falling shadows

Hashem Bordba, Xiao Long Xin, Rajab Ali Borzooei, Young Bae Jun
<span title="2022-02-11">2022</span> <i title="Zenodo"> Zenodo </i> &nbsp;
In this article, we apply the notion of neutrosophic set theory to (positive implicative) ideals in BCK-algebras by using the concept of falling shadows.  ...  Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics.  ...  pointed out the equivalence of a fuzzy set and a class of random sets. Wang and Sanchez [?] introduced the theory of falling shadows which directly relates probability concepts to the membership H.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.6041289">doi:10.5281/zenodo.6041289</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3tyajhgagrfnvg5cvmrwsrodei">fatcat:3tyajhgagrfnvg5cvmrwsrodei</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220505175554/https://zenodo.org/record/6041290/files/PositiveImplicativeNeutrosophic2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bc/86/bc86929f62c5cbf772a027e63bfa3beab016146b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.6041289"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> zenodo.org </button> </a>
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