Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
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TL;DR: In this article, a membership criterion for numerical semigroups generated by generalized arithmetic sequences is presented, and fundamental questions concerning a numerical semigroup such as computing the Frobenius number and determining whether the numercial semigroup is symmetric.
Abstract: We study numerical semigroups generated by generalized arithmetic sequences. We present a membership criterion for such a numerical semigroup, and by this we are able to answer fundamental questions concerning a numerical semigroup such as computing the Frobenius number and the type of the numerical semigroup, and decide whether the numercial semigroup is symmetric. Also for this kind of numerical semigroups, we compute the cardinality of a minimal presentation and determine whether they are complete intersections.
10 citations
TL;DR: In this paper, the authors modify the wreath product given by Neumann and Preston to study the structure of generalized Clifford semigroups and prove that a semigroup is a left C-rpp semigroup if and only if it is the Wreath product of a left regular band and a C-Rpp semiigroup.
Abstract: The concept of wreath product of semigroups was first introduced by Neumann in 1960, and later on, this concept was used by Preston to investigate the structure of some inverse semigroups. In this paper, we modify the wreath product given by Neumann and Preston to study the structure of some generalized Clifford semigroups. In particular, we prove that a semigroup is a left C-rpp semigroup if and only if it is the wreath product of a left regular band and a C-rpp semigroup. Our result provides a new insight to the structure of left C-rpp semigroups.
9 citations
TL;DR: In this article, it was shown that the semigroup algebra of an ample semigroup over a field is Frobenius if and only if it is a finite inverse semigroup.
Abstract: We prove that the semigroup algebra of an ample semigroup \(S\) over a field is Frobenius if and only if \(S\) is a finite inverse semigroup.
9 citations
TL;DR: In this paper, the authors provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space.
Abstract: In this manuscript we provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators.
9 citations
TL;DR: In this paper, the authors characterize Cohen-Macaulay and Gorenstein rings obtained from certain types of convex body semigroups and provide algorithms to check if a polygonal or circle semigroup is CoMHA/Gorenstein.
Abstract: We characterize Cohen-Macaulay and Gorenstein rings obtained from certain types of convex body semigroups. Algorithmic methods to check if a polygonal or circle semigroup is Cohen-Macaulay/Gorenstein are given. We also provide some families of Cohen-Macaulay and Gorenstein rings.
9 citations