Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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10 citations
TL;DR: In this article, a combinatorial counterpart of the Cohen-Macaulay duality on a class of curve singularities was established, which includes algebroid curves, and the good semigroup duality was shown to be compatible under taking values.
Abstract: We establish a combinatorial counterpart of the Cohen-Macaulay duality on a class of curve singularities which includes algebroid curves. For such singularities the value semigroup and the value semigroup ideals of all fractional ideals satisfy axioms that define so-called good semigroups and good semigroup ideals. We prove that each good semigroup admits a canonical good semigroup ideal which gives rise to a duality on good semigroup ideals. We show that the Cohen-Macaulay duality and our good semigroup duality are compatible under taking values.
10 citations
TL;DR: In this paper, the authors study the internal structure of C*-algebras associated to a left cancellative semigroup in which any two principal right ideals are either disjoint or intersect in another principal right ideal; these are variously called right LCM semigroup or semigroups that satisfy Clifford's condition.
Abstract: We initiate the study of the internal structure of C*-algebras associated to a left cancellative semigroup in which any two principal right ideals are either disjoint or intersect in another principal right ideal; these are variously called right LCM semigroups or semigroups that satisfy Clifford's condition. Our main findings are results about uniqueness of the full semigroup C*-algebra. We build our analysis upon a rich interaction between the group of units of the semigroup and the family of constructible right ideals. As an application we identify algebraic conditions on S under which C*(S) is purely infinite and simple.
10 citations
TL;DR: In this paper, it was shown that the lattice of congruences on a regular semigroup S contains certain fundamental congruence, such as minimum band congruencies β and β-congruences β, which is the same if they have the same meet and join with β. This result enabled them to characterize θ-modular bands of groups as precisely those bands for which ρ(ρ∨β, ρ∧β) is an embedding of S into a product of sublattices.
Abstract: It is well known that the lattice Λ(S) of congruences on a regular semigroup S contains certain fundamental congruences. For example there is always a minimum band congruence β, which Spitznagel has used in his study of the lattice of congruences on a band of groups [16]. Of key importance to his investigation is the fact that β separates congruences on a band of groups in the sense that two congruences are the same if they have the same meet and join with β. This result enabled him to characterize θ-modular bands of groups as precisely those bands of groups for which ρ(ρ∨β, ρ∧β)is an embedding of Λ(S) into a product of sublattices.
10 citations
Journal Article•
TL;DR: In this article, the Betti numbers of the numerical semigroup ring K[T ] were studied when S is a 3-generated semigroup or telescopic. And they were studied for 4-generated symmetric semigroups and the so-called 4-irreducible numerical semigroup.
Abstract: For any numerical semigroup S, there are infinitely many numerical symmetric semigroups T such that S = T/2 (see below for the definition of T/2) is their half. We are studying the Betti numbers of the numerical semigroup ring K[T ] when S is a 3-generated numerical semigroup or telescopic. We also consider 4-generated symmetric semigroups and the so called 4-irreducible numerical semigroups.
10 citations