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 paper, a continuous monadic functor T in the category of Tychonov spaces for each discrete topological semigroup X is extended to a right-topological semiigroup operation on TX whose topological center contains the dense subsemigroup of all elements of TX that have finite support.
Abstract: Given a continuous monadic functor T in the category of Tychonov spaces for each discrete topological semigroup X we extend the semigroup operation of X to a right-topological semigroup operation on TX whose topological center contains the dense subsemigroup of all elements of TX that have finite support.
2 citations
Journal Article•
TL;DR: In this article, the authors define a congruence on inverse semi-group S such that amenability of S is equivalent to amenability for S/S/S. The main difference is that the corresponding homomorphic image is a Cliord semigroup rather than a discrete group.
Abstract: In this paper we define a congruence on inverse semi- group S such that amenability of S is equivalent to amenability of S/ . We study module amenability of semigroup algebra l 1 (S/ ) when S is an inverse semigroup with idempotents E and prove that it is equivalent to module amenability of l 1 (S). The main dierence of this action with the more studied trivial action is that in this case the corresponding homomorphic image is a Cliord semigroup rather than a discrete group.
2 citations
Journal Article•
TL;DR: In this paper, the multiplicative semigroup of Z_m is studied and the problem concerning the powers of a subset of the semigroups of Zm(m) is studied.
Abstract: In several papers Paul Dubreil has studied the multiplicative semigroup of several types of rings and conditions for semigroups which can serve as an underlying semigroup of a ring. In this paper we shall deal with the multiplicative semigroup of $Z_m$, which will be denoted by $S(m)$, and we shall treat a rather unconventional problem concerning the powers of a subset of $S(m)$.
2 citations
2 citations
TL;DR: In this article, the authors present a new technique for studying the dynamics of a finitely generated rational semigroup and derive a sharp bound for the Hausdorff dimension of the Julia set of such a semigroup.
Abstract: In this paper, we present a new technique for studying the dynamics of a finitely generated rational semigroup. Such a semigroup can be associated naturally to a certain holomorphic correspondence on $\mathbb{P}^1$. Then, results on the iterative dynamics of such a correspondence can be applied to the study of the rational semigroup. We focus on a certain invariant measure for the aforementioned correspondence---known as the equilibrium measure. This confers some advantages over many of the known techniques for studying the dynamics of rational semigroups. We use the equilibrium measure to analyse the distribution of repelling fixed points of a finitely generated rational semigroup, and to derive a sharp bound for the Hausdorff dimension of the Julia set of such a semigroup.
2 citations