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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6 citations
Posted Content•
TL;DR: In this paper, it was shown that almost all cancellative triple systems with vertex set [n] are tripartite, which sharpens a theorem of Nagle and Rodl on the number of cancellative three systems.
Abstract: A triple system is cancellative if no three of its distinct edges satisfy $A \cup B=A \cup C$. It is tripartite if it has a vertex partition into three parts such that every edge has exactly one point in each part. It is easy to see that every tripartite triple system is cancellative. We prove that almost all cancellative triple systems with vertex set [n] are tripartite. This sharpens a theorem of Nagle and Rodl on the number of cancellative triple systems. It also extends recent work of Person and Schacht who proved a similar result for triple systems without the Fano configuration. Our proof uses the hypergraph regularity lemma of Frankl and Rodl, and a stability theorem for cancellative triple systems due to Keevash and the second author.
6 citations
TL;DR: In this paper, the authors give procedures for determining whether a given monoid is an affine semigroup and for computing the dual of a semigroup, and also give methods for deciding whether an affined semigroup is normal and/or full.
6 citations
Journal Article•
TL;DR: In this article, it was shown that the localization of a semigroup ring R[X;S] is a TV-PVMD if and only if R is a Torsion Free Cancellative Semigroup with zero.
Abstract: We give several characterizations of a TV-PVMD and we show that the localization R[X;S] of a semigroup ring R[X;S] is a TV-PVMD if and only if R is a TV-PVMD where and S is a torsion free cancellative semigroup with zero.
6 citations
TL;DR: Theorem 3.3 as mentioned in this paper states that a semigroup ring is Artian if and only if R is unitary and S is not idempotent, while Theorem 2.3 states that R[S] is noetherian if S and (R, + ), the additive group of R, are finitely generated.
6 citations