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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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Miyuki Yamada1
TL;DR: In this article, it was shown that a regular semigroup S becomes a regular *-semigroup (in the sense of [1]) if and only if S has a certain subset called a p-system.
Abstract: In this paper, firstly it is shown that a regular semigroup S becomes a regular *-semigroup (in the sense of [1]) if and only if S has a certain subset called a p-system. Secondly, all the normal *-bands are completely described in terms of rectangular *-bands (square bands) and transitive systems of homomorphisms of rectangular *-bands. Further, it is shown that an orthodox semigroup S becomes a regular *-semigroup if there is a p-system F of the band ES of idempotents of S such that F∋e, ES∋t, e≥t imply t∈F. By using this result, it is also shown that F is a p-system of a generalized inverse semigroup S if and only if F is a p-system of FS.

16 citations

Journal ArticleDOI
TL;DR: In this article, the hypercyclicity of the translation group on the weighted spaces was shown to be Ω(L^p_\rho(\mathbb R,\mathbb C)$ for admissible weight.
Abstract: In this note we extend the hypercyclicity criterion (HC) to $C_0$- semigroups on separable Banach spaces and characterize semigroups satisfying (HC). Using (HC) we show the hypercyclicity of the translation group on the weighted spaces $L^p_\rho(\mathbb R,\mathbb C)$ or $C_{0,\rho}(\mathbb R,\mathbb C)$ for admissible weight functions $\rho$.

16 citations

Journal ArticleDOI
TL;DR: In this article, the ω-value of the generators of any numerical semigroup with embedding dimension three is determined, and all possible orderings of the generator's ω values are determined.
Abstract: In this paper, we find the ω-value of the generators of any numerical semigroup with embedding dimension three. This allows us to determine all possible orderings of the ω-values of the generators. In addition, we relate the ω-value of the numerical semigroup to its catenary degree.

16 citations

Journal ArticleDOI
TL;DR: The notion of semigroup with a tight ideal series was introduced in this article, and its algebraic closure in semitopological inverse semigroups with continuous inversion was studied.
Abstract: We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations $\mathscr{I}_\lambda^n$ of the rank $\leqslant n$ is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. We also derive related results about the nonexistence of (partial) compactifications of classes of semigroups that we consider.

16 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20238
202224
20216
20206
20193
201810