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Combinatorics of involutive divisions
[article]

2017
*
arXiv
*
pre-print

In order to deal with this problem, we introduce two

arXiv:1707.02452v1
fatcat:a24sakuvdzcxfbwyhnww6bc7ei
*graphs*as tools, one is strictly related to Seiler's L-*graph*, whereas the second*generalizes*it, to cover the case of "non-continuous" (in the sense ... Indeed, given an element in the ideal (resp. escalier), walking backwards (resp. forward) in the*graph*, we can identify all the other*generators*of the ideal (resp. elements of degree D in the escalier ... : 1. there are no oriented paths from t to s; lcm(s, t) ∈ C L (t, U) We call such*a**graph**a**generalized**Ufnarovsky*-like*graph*. ...##
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On the Calculation of gl.dimG^N(A) and gl.dimA by Using Gröbner Bases
[article]

2008
*
arXiv
*
pre-print

It is shown how to use the

arXiv:0805.0686v1
fatcat:cf5en46drbamhl3qbrxifopvea
*Ufnarovski**graph*Γ ( LM( G)) and the*graph*of n-chains Γ_ C( LM( G)) to calculate gl.dimG^N(*A*) and gl.dimA, where G^N(*A*), respectively*A*, is the associated N-graded algebra of ... Let*A*=K< X_1,...,X_n> /< G> be*a*K-algebra defined by*a*finite Gröbner basis G. ... Then the*Ufnarovski**graph*of Ω (introduced by V. ...##
###
GROWTH OF FINITELY PRESENTED REES QUOTIENTS OF FREE INVERSE SEMIGROUPS

2011
*
International journal of algebra and computation
*

of primitive words that label loops of the

doi:10.1142/s0218196711006182
fatcat:y2juryf73jdofcrc226xutgsom
*Ufnarovsky**graph*of the presentation. [25] J. ... Wolf, "Growth of finitely*generated*solvable groups and curvature of Riemannian manifolds", J. Differential Geom. 2 (1968), 421-446. ... 1) for some primitive word z that labels*a*loop of the*Ufnarovsky**graph*. ...##
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Page 6017 of Mathematical Reviews Vol. , Issue 2004h
[page]

2004
*
Mathematical Reviews
*

by computer algebra (217-223); Peter Schenzel, On curves of small degree on

*a*nor- mal rational surface scroll (225-239); Anna Torstensson, Victor*Ufnarovski*[V. ... Dobbs, Marco Fontana and Gabriel Picavet,*Generalized*going-down homomorphisms of commutative rings (143-163); Said El Baghdadi, The class group of the composite ring of*a*pair of Krull domains and applications ...##
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Entropy of monomial algebras and derived categories
[article]

2021
*
arXiv
*
pre-print

Moreover, we relate these two kinds of entropy with the topological entropy of the

arXiv:2103.03946v1
fatcat:7xlh7vrmdjax5bui3t53566334
*Ufnarovski**graph*of*A*and the entropy of the path algebra of the*graph*. ... Let*A*be*a*finitely presented associative monomial algebra. We study the category qgr(*A*) which is*a*quotient of the category of graded finitely presented*A*-modules by the finite-dimensional ones. ... Moreover, h(L) is equal to the topological entropy h(Q*A*) of the*Ufnarovski**graph*Q*A*of*A*. ...##
###
Regular Gröbner Bases

2002
*
Journal of symbolic computation
*

In this paper we introduce the concept of bi-automaton algebras,

doi:10.1006/jsco.2001.0500
fatcat:saohwxqd6re6lnvbjhtr2l7dbm
*generalizing*the automaton algebras previously defined by*Ufnarovski*. ...*A*bi-automaton algebra is*a*quotient of the free algebra, defined by*a*binomial ideal admitting*a*Gröbner basis which can be encoded as*a*regular set; we call such*a*Gröbner basis regular. ... According to the proof of Theorem 9(d) in*Ufnarovski*(1989) , the finite union G = ∪ x,y∈P {xwy − yxw | w ∈ c * y } is*a*Gröbner basis for the ideal*generated*by the present commutators. ...##
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Page 2065 of Mathematical Reviews Vol. , Issue 96d
[page]

1996
*
Mathematical Reviews
*

Victor

*A*.*Ufnarovski*(Lund) 96d:13043 13P10 Ramella, Isabella (I- NAPL-AM; Naples) Ideals of points in*generic*position:*a*polynomial algorithm for computing*a*minimal set of*generators*. ... Alessandro Logar (Trieste) 96d:13042 13P10 0SC15 de Loera, Jestis*A*. (1-CRNL-AM; Ithaca, NY) Grébner bases and*graph*colorings. (English summary) Beitrége Algebra Geom. 36 (1995), no. 1, 89-96. ...##
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Page 2540 of Mathematical Reviews Vol. , Issue 94e
[page]

1994
*
Mathematical Reviews
*

Lopez-Permouth,

*A*survey on the theory of weakly-injective modules (205-232); Todd C. Torgersen, Distributing symbolic computations on*a*net- work of workstations (233-246); V.*A*.*Ufnarovski*[V.*A*. ... Summary: “Let*A*= M — N be*a*regular splitting of an M-matrix. We give some equivalent properties which are equivalent to*graph*compatible splittings. ...##
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Page 497 of Mathematical Reviews Vol. , Issue 99a
[page]

1991
*
Mathematical Reviews
*

Green], Teo Mora and Victor

*Ufnarovski*[V.*A*. Uf- narovskii], The non-commutative Grébner freaks (93-104); Ben- jamin J. ... Akl, Spanning subgraphs with applications to communi- cation on*a*subclass of the Cayley-*graph*-based networks (79-96); Luisa Gargano, Adele*A*. ...##
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Non-commutative computer algebra and molecular computing

2001
*
Computer Science Journal of Moldova
*

The main idea is that one can get more advantage in using molecular computing for non-commutative computer algebra compared with

doaj:0b760cb230f64ca6bbb2ba8f45516165
fatcat:eq64fnnxfzd5fpx7hcazk62jcy
*a*commutative one. ... But what is more important that*a*free subgroup with*a*larger number of*generators*(even infinitely many) is simply*a*subgroup of our 2-*generated*group. ... Among them the most popular are the algorithms for the different*graphs*problems, SAT problem, the data encryption breaking etc. ...##
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Page 111 of Mathematical Reviews Vol. , Issue 96a
[page]

1996
*
Mathematical Reviews
*

More precisely, given

*a*non-oriented, loop-free*graph**A*C X x X, the associated algebra R(X4) = (Llc R(x))/(ab — ba|*a*€ R(x), b € R(y), (x,y) €*A*) is considered. ... Let*A*be an algebra*generated*by the finite alphabet X. Let w be*a*word in this alphabet that is maximal in the lexicographical ordering in the set of words that correspond to nonzero elements in*A*. ...##
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BERGMAN under MS-DOS and Anick's resolution

1997
*
Discrete Mathematics & Theoretical Computer Science
*

*A*table is provided permitting

*a*comparison of the effectiveness of the calculations in BERGMAN with the other systems. ... International audience Noncommutative algebras, defined by the

*generators*and relations, are considered. ... Let us consider

*a*

*graph*=(V;E); where the set of vertex consists of the union of the unit 1; alphabet X and all proper suffixes of the obstructions. ...

##
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Page 3053 of Mathematical Reviews Vol. , Issue 99e
[page]

1999
*
Mathematical Reviews
*

To any undirected

*graph**A*, Gel/fand and Ponomarev introduced*a*preprojective algebra P(*A*); it is finite-dimensional over*a*field K if and only if*A*is*a*disjoint union of Dynkin diagrams. ... [Cojocaru, Svetlana] (MO-AOS; Chisinau) ;*Ufnarovski*, V. [Ufnarovskii, V.*A*.] (MO-AOS; Chisinau BERGMAN under MS-DOS and Anick’s resolution. (English summary) Lie computations (Marseille, 1994). ...##
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Algebras and their Associated Monomial Algebras
[article]

2006
*
arXiv
*
pre-print

) is the associated Γ-graded K-algebra of

arXiv:math/0609583v1
fatcat:msj2ksc5ljaxzntfsnxe7q424u
*A*defined by FA, and < HT(I)> is the Γ-graded ideal of R*generated*by the set of head terms of I. ... Considering the Γ-grading filtration FR of R and the Γ-filtration FA induced by FR for the quotient K-algebra*A*=R/I, we show that there is*a*Γ-graded K-algebra isomorphism G(*A*)*A̅*=R/< HT (I)>, where G(*A*... Realization via Gröbner Bases and*Ufnarovski**Graphs*Convention throughout the paper Let K be*a*field. ...##
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Noetherianity and Ext

2008
*
Journal of Pure and Applied Algebra
*

Let R = R 0 ⊕ R 1 ⊕ R 2 ⊕ · · · be

doi:10.1016/j.jpaa.2007.10.011
fatcat:k6r6gitxm5bexjgkl3qagbm3wu
*a*graded algebra over*a*field K such that R 0 is*a*finite product of copies of K and each R i is finite dimensional over K . ... We pay particular attention to the case when R is*a*Koszul algebra and S is the Koszul dual to R. ... Moreover, since R is*a*Koszul algebra and S has the same quiver as R and relations*generated*by all the paths of length 2 not in ρ, we see that the relation*graph*of S is, in fact, the*Ufnarovski**graph*...
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