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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TL;DR: In this paper, it was shown that if such an operator $A$ generates a semigroup of composition operators, then it is automatically a composition operator, so that the condition of quasicontractivity of the semigroup in the cited result is not necessary.
Abstract: Avicou, Chalendar and Partington proved that an (unbounded) operator $(Af)=G\cdot f'$ on the classical Hardy space generates a $C_0$ semigroup of composition operators if and only if it generates a quasicontractive semigroup. Here we prove that if such an operator $A$ generates a $C_0$ semigroup, then it is automatically a semigroup of composition operators, so that the condition of quasicontractivity of the semigroup in the cited result is not necessary. Our result applies to a rather general class of Banach spaces of analytic functions in the unit disc.
10 citations
TL;DR: In this article, the minimal degree of an inverse semigroup S is defined as the cardinality of a set A such that S is isomorphic to an inverse semiigroup of one-to-one partial transformations of A.
Abstract: The minimal degree of an inverse semigroup S is the minimal cardinality of a set A such that S is isomorphic to an inverse semigroup of one-to-one partial transformations of A. The main result is a formula that expresses the minimal degree of a finite inverse semigroup S in terms of certain subgroups and the ordered structure of S. In fact, a representation of S by one-to-one partial transformations of the smallest possible set A is explicitly constructed in the proof of the formula. All known and some new results on the minimal degree follow as easy corollaries
10 citations
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