Showing papers on "Cancellative semigroup published in 1998"
TL;DR: In this article, the structure of a semigroup S generated by a permutation group G of units and an idempotent ϵ is studied and it is shown that S is a regular semigroup.
Abstract: It is well known that the semigroup of all transformations on a finite set X of order n is generated by its group of units, the symmetric group, and any idempotent of rank n − 1. Similarly, the symmetric inverse semigroup on X is generated by its group of units and any idempotent of rank n − 1 while the analogous result is true for the semigroup of all n × n matrices over a field. In this paper we begin a systematic study of the structure of a semigroup S generated by its group G of units and an idempotent ϵ . The first section consists of preliminaries while the second contains some general results which provide the setting for those which follow. In the third section we shall investigate the situation where G is a permutation group on a set X of order n and ϵ is an idempotent of rank n − 1. In particular, we shall show that any such semigroup S is regular. Furthermore we shall determine when S is an inverse or orthodox semigroup or completely regular semigroup. The fourth section deals with a special ca...
76 citations
TL;DR: In this article, a new representation of the generator of a subordinate semigroup as a limit of bounded operators is presented, where the generator is viewed as a function of a generator of the original semigroup.
Abstract: We prove a new representation of the generator of a subordinate semigroup as limit of bounded operators. Our construction yields, in particular, a characterization of the domain of the generator. The generator of a subordinate semigroup can be viewed as a function of the generator of the original semigroup. For a large class these functions we show that operations at the level of functions has its counterpart at the level of operators.
75 citations
TL;DR: For a semigroup S and a set B, the relative rank of S modulo A is the minimal cardinality of a setB such that S can be generated.
Abstract: For a semigroup S and a set the relative rank of S modulo A is the minimal cardinality of a setB such that generates S. We show that the relative rank of an infinite full transformation semigroup modulo the symmetric group, and also modulo the set of all idempotent mappings, is equal to 2. We also characterise all pairs of mappings which, together with the symmetric group or the set of all idempotents, generate the full transformation semigroup.
70 citations
TL;DR: In this article, the authors characterize the semigroups with CEP by a set of conditions on their structure, and show that every such semigroup is a semilattice of nil extensions of rectangular groups.
Abstract: on a semigroup of T of S extends to the semigroup S, if there exists a congruence ρ on s such that ρ|T= ρT. A semigroup S has the congruence extension property, CEP, if each congruence on each semigroup extends to S. In this paper we characterize the semigroups with CEP by a set of conditions on their structure (by this we answer a problem put forward in [1]). In particular, every such semigroup is a semilattice of nil extensions of rectangular groups.
12 citations
Journal Article•
8 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: In this article, it was shown that a given pair (A, B) generates a B-bounded semigroup if and only if in a certain extrapolation space related to the operator B, the closure of A generates a semigroup.
Abstract: In [3]A. Bellini-Morante defined and analysed a new one-parameter family of bounded operators which he called a B-bounded semigroup. The definition was motivated by an example from the transport theory where the evolution generated by an operator A was in a certain sense controlled by another operator B. In this paper we show that a given pair (A, B) generates a B-bounded semigroup if and only if in a certain extrapolation space related to the operator B, the closure of A generates a semigroup and we also address some related topics.
6 citations
TL;DR: The Mobius semigroup studied in this paper arises naturally geometrically as the (compression) subsemigroup of the group of Mobius transformations which carry some fixed open Mobius ball into itself.
Abstract: The Mobius semigroup studied in this paper arises very naturally geometrically as the (compression) subsemigroup of the group of Mobius transformations which carry some fixed open Mobius ball into itself. It is shown, using geometric arguments, that this semigroup is a maximal subsemigroup. A detailed analysis of the semigroup is carried out via the Lorentz representation, in which the semigroup resurfaces as the semigroup carrying a fixed half of a Lorentzian cone into itself. Close ties with the Lie theory of semigroups are established by showing that the semigroup in question admits the structure of an Ol'shanskii semigroup, the most widely studied class of Lie semigroups.
5 citations
TL;DR: In this paper, it was shown that if a finitely presented Rees quotient of a free inverse semigroup has polynomial growth, then its growth series is in a certain subsemiring of N [[z]].
4 citations
TL;DR: In this article, it was shown that the subset of freek-generated subsemigroups of the semigroup of all automaton transformations over a finite alphabet is a second category set (in the sense of the Baire category approach).
Abstract: It is established that the subset of freek-generated subsemigroups of the semigroup of all automaton transformations over a finite alphabet is a second category set (in the sense of the Baire category approach) in the set of allk-generated subsemigroups. A continuum series of pairs of automaton transformations each of which generates a free semigroup of rank two is indicated. A criterion is established for this semigroup to be a finite-automaton group.
4 citations
TL;DR: In this paper, the structure of the semigroup S is investigated when RS admits a compact topology and it is proved that the last principal factors of S have finitely many of right or left ideals.
Abstract: The structure of the semigroup S is investigated when the semigroup ring RS admits a compact topology. It is proved that, in case of the semisimple semigroup S , the ”last” principal factors of S have finitely many of right or left ideals. It is shown that it is not true for other factors.
TL;DR: In this article, the authors studied the semigroup generated by the set of the kemel-trace operators on the congruence lattice of a primitive regular semigroup, which is best described as an orthogonal sum of completely 0-simple semigroups.
Abstract: The aim of this paper is the study of the semigroup generated by the set of the kemel-trace operators on the congruence lattice of a primitive regular semigroup. Since the structure of the nontrivial primitive regular semigroups is best described as an orthogonal sum of completely 0-simple semigroups, the problem of describing the previous semigroup is solved by determining the semigroups associated with any semigroup of the orthogonal sum. To do the latter, use is made of the Rees Theorem.