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 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
TL;DR: In this article, it was shown that a compact Clifford topological semigroup S is metrizable if and only if the set E =e∈S:ee=e of idempotents of S is a Gδ-set in S.
Abstract: We prove that a countably compact Clifford topological semigroup S is metrizable if and only if the set E={e∈S:ee=e} of idempotents of S is a metrizable Gδ-set in S.
2 citations
Journal Article•
TL;DR: In this article, the intra-regular -semigroup and the relation based on bi-ideals, quasi-ideal, and ideals right and left are discussed and discussed in detail.
Abstract: . A -semigroup is generalization from semigroup, which concepts in -semigroup analogue with concepts in semigroup. is called a -semigroup if there is a mapping between two nonempty sets and , written as , such that , for all and . A -semigroup is said to be intra-regular if contains for all elements of intra regular, is if , for all and . In this paper, discussed about intra-regular -semigroup and the relation based on bi-ideals, quasi-ideals, and ideals right and left.
2 citations
22 May 2013
TL;DR: It is shown that this set of equtional classes of finite functions endowed with the operation of class composition constitutes a topological semigroup that is profinite.
Abstract: We consider the set of equtional classes of finite functions endowed with the operation of class composition. Thus defined, this set gains a semigroup structure. This paper is a contribution to the understanding of this semigroup. We present several interesting properties of this semigroup. In particular, we show that it constitutes a topological semigroup that is profinite.
2 citations
01 Jan 1972
2 citations