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MINIMAL EXPANSIONS OF SEMILATTICES
2004
International journal of algebra and computation
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The results involve the investigation of some minimal expansions of semilattices. ...
We determine the minimal extension of the sequence 0, 1, 1, . . . , 1, 2 . This completes and extends the work of K. M. ...
On the basis of this lemma, we will refer to an algebra that represents the length m + 1 sequence 0, 1, . . . , 1, 2 as an m-ary semilattice expansion. ...
doi:10.1142/s0218196704001852
fatcat:k4skwofk3jatrk2xbfvfkh6lfm
Page 205 of Mathematical Reviews Vol. , Issue 2000a
[page]
2000
Mathematical Reviews
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Once again the particular case of semilattices leads to an expansion which corresponds to a known expansion $2) due to K. Henckell. ...
The so-called Karnofsky-Rhodes expansion fits under this heading, while expanding by the variety of semilattices is the same as applying the Cayley expansion. ...
Page 6368 of Mathematical Reviews Vol. , Issue 2002I
[page]
2002
Mathematical Reviews
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An example of a planar, rank-connected lattice that is not admissible is given.”
2002i:06004 06A12 06A06
McElwee, Brett (5-SYD-SM; Sydney)
Maximal and minimal semilattices on ordered sets. ...
non- expansive multiplier; (2) f is a multiplicative operator; (3) f isa quasi-interior operator. ...
Medians, lattices, and trees
1954
Proceedings of the American Mathematical Society
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In other papers [3; 4]2 the author discussed the behavior of medians, segments, and betweenness in systems called median semilattices. A tree is a type of median semilattice. ...
In a semilattice an upper bound of a and b is an element / such that a=at and b = bt. ...
The extension T of 5 which has been described is minimal in the sense that a distributive lattice containing 5 contains a sublattice isomorphic to T. ...
doi:10.1090/s0002-9939-1954-0064750-3
fatcat:zbsahadv2ne6jfcccyyyxrblrm
Page 06 of Mathematical Reviews Vol. , Issue 90C
[page]
1990
Mathematical Reviews
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The minimal k with the above property is called the Boolean dimension dima,(P) of P. We present a universal upper bound for the Boolean dimen- sion of posets. ...
The blocks of
the inverse matrix immediately give the wanted expansion. Heinrich Niederhausen (1-FLAT)
90c:06007 06A10 Rus, Ioan A. ...
Monads and Quantitative Equational Theories for Nondeterminism and Probability
2020
International Conference on Concurrency Theory
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Our main result is the presentation of this lifted monad in terms of the quantitative equational theory of convex semilattices, using the framework of quantitative algebras recently introduced by Mardare ...
The monad of convex sets of probability distributions is a well-known tool for modelling the combination of nondeterministic and probabilistic computational effects. ...
We need to verify that F(f ) is a morphisms in QA(QTh CS ), i.e., a non-expansive homomorphism of convex semilattices (see Definition 22) . ...
doi:10.4230/lipics.concur.2020.28
dblp:conf/concur/MioV20
fatcat:lxbn2qhbffht5kto36awdzsvqm
Monads and Quantitative Equational Theories for Nondeterminism and Probability
[article]
2020
arXiv
pre-print
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Our main result is the presentation of this lifted monad in terms of the quantitative equational theory of convex semilattices, using the framework of quantitative algebras recently introduced by Mardare ...
The monad of convex sets of probability distributions is a well-known tool for modelling the combination of nondeterministic and probabilistic computational effects. ...
We want to prove that whenever f : ((X, d), α) → ((Y, d ), β) is a non-expansive morphism of Eilenberg-Moore algebras then F(f ) is a non-expansive homomorphism of convex semilattices. ...
arXiv:2005.07509v1
fatcat:4oqtddfruvfurkga7h6nrmwg5y
Page 63 of Mathematical Reviews Vol. , Issue 91K
[page]
1991
Mathematical Reviews
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The author studies the convexity structure in the space of all order
arcs of a semilattice. He obtains three main theorems. ...
The first gives some simple conditions under which an arc of a semilattice is mapped back into itself by an order-preserving function. ...
The Ramsey and the ordering property for classes of lattices and semilattices
[article]
2018
arXiv
pre-print
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It now comes as no surprise that the same is true for varieties of semilattices. ...
We show that for almost all nontrivial locally finite varieties of lattices no "reasonable" expansion of the finite members of the variety by linear orders gives rise to a Ramsey class. ...
The author gratefully acknowledges the support of the Ministry of Science, Education and Technological Development of the Republic of Serbia, Grant No. 174019. ...
arXiv:1802.00979v1
fatcat:frmcij5yjjedtelqw4b3zq7nxq
Page 158 of Mathematical Reviews Vol. , Issue 90A
[page]
1990
Mathematical Reviews
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Minimal non-finitely based varieties are called limit varieties. All previously discovered limit varieties of semigroups are homotypical (contain the variety of semilattices). ...
An expansion of S (or, more precisely, an expansion of the morphism /: A* — S, where f denotes the free semigroup on A) is a morphism g: A* — T such that f = hg for some surjective morphism /: T — S. ...
The median function on median graphs and semilattices
2000
Discrete Applied Mathematics
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In this paper a new characterization of the median function is given for G a median graph. This is used to give a characterization of the median function on median semilattices. ? ...
A median of a k-tuple = (x 1; : : : ; x k ) of vertices of a ÿnite connected graph G is a vertex x for which k i=1 d(x; xi) is minimum, where d is the geodesic metric on G. ...
An important feature which follows from the proof of Theorem 1 is that in obtaining a graph G from a median graph H by a succession of expansions, the expansions can be applied in any order. ...
doi:10.1016/s0166-218x(99)00208-5
fatcat:ve72ryvzcfcephqrsepmxq5ace
Page 2396 of Mathematical Reviews Vol. , Issue 87e
[page]
1987
Mathematical Reviews
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For instance, S is a left group if and only if B(S) is a left zero band; S is a semilattice of groups if and only if B(S) is a commutative regular semigroup (or, equivalently, B(S) is a semilattice). ...
The minimal right congruences of
a semigroup are classified into three types 21, N2, N3 according
to the conditions (1), (2), (3). ...
On semilattices and lattices for families of theories
[article]
2017
arXiv
pre-print
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We define and study semilattices and lattices for E-closed families of theories. Properties of these semilattices and lattices are investigated. ...
It is shown that lattices for families of theories with least generating sets are distributive. ...
By the definition, an e-minimal structure A ′ consists of E-classes with a minimal set TH(A ′ ). If TH(A ′ ) is the least for models of Th(A ′ ) then A ′ is called e-least. Definition [2] . ...
arXiv:1701.00208v2
fatcat:3wwi7i2htndvnb2ti4fnmyv72u
On tolerances representable as R ∘ R^-
[article]
2006
arXiv
pre-print
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(ii) Consider the semilattice S with 6 minimal elements a, b 1 , b 2 , b 3 , b 4 , c and with a largest element 1. ...
If x, y are minimal elements of S and both x R 1 and y R 1, then x R • R − y, hence x Θ y. ...
arXiv:math/0610091v1
fatcat:3vad55pyivb47olyuxzcbknzoy
Recent Results on the Algebraic Approach to the CSP
[chapter]
2008
Lecture Notes in Computer Science
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We describe an algebraic approach to the constraint satisfaction problem (CSP) and present recent results on the CSP that make use of, in an essential way, this algebraic framework. ...
; a contradiction with minimality of B. ...
Let A be a finite algebra and α a minimal congruence of A. ...
doi:10.1007/978-3-540-92800-3_4
fatcat:x56vxo4fobadjmeayv3k35atgi
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