Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
Papers published on a yearly basis
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TL;DR: In this article, the relationship between the ring and its circle semigroup is investigated, where the ring is simple, 0-simple, cancellative, 0 -cancellative, regular, inverse or union of groups.
Abstract: Let R be a ring and define x ○ y = x + y - xy, which yields a monoid (R, ○), called the circle semigroup of R. This paper investigates the relationship between the ring and its circle semigroup. Of particular interest are the cases where the semigroup is simple, 0-simple, cancellative, 0-cancellative, regular, inverse, or the union of groups, or where the ring is simple, regular, or a domain. The idempotents in R coincide with the idempotents in (R, ○) and play an important role in the theory developed.
4 citations
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TL;DR: In this paper, it was shown that the semigroup algebra is always a 2n-weakly module amenable as an inverse semigroup with the set of idempotents $E$.
Abstract: Let $S$ be an inverse semigroup with the set of idempotents $E$. We prove that the semigroup algebra $\ell^{1}(S)$ is always $2n$-weakly module amenable as an $\ell^{1}(E)$-module, for any $n\in \mathbb{N}$, where $E$ acts on $S$ trivially from the left and by multiplication from the right.
4 citations
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4 citations
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01 Jan 2011TL;DR: The class (resp., t-class) semigroup is the semigroup of the isomorphy classes of the nonzero fractional ideals with the operation induced by ideal (t-) multiplication.
Abstract: The class (resp., t-class) semigroup of an integral domain is the semigroup of the isomorphy classes of the nonzero fractional ideals (resp., t-ideals) with the operation induced by ideal (t-) multiplication. This paper surveys recent literature which studies ring-theoretic conditions that reflect reciprocally in the Clifford property of the class (resp., t-class) semigroup. Precisely, it examines integral domains with Clifford class (resp., t-class) semigroup and describes their idempotent elements and the structure of their associated constituent groups.
4 citations
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TL;DR: In this paper, it was shown that every non-degenerate irreducible homomorphism from the multiplicative semigroup of all n-by-n matrices over an algebraically closed field of characteristic zero to the semigroup m-bym matrices is reducible.
4 citations