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: It is shown that its transition semigroup is the syntactic semigroup of the language recognized by the automaton, and an inverse limit of the partial semigroups of nonzero regular elements of their transition semig groups is described.
Abstract: Rauzy graphs of subshifts are endowed with an automaton structure. For Sturmian subshifts, it is shown that its transition semigroup is the syntactic semigroup of the language recognized by the automaton. An inverse limit of the partial semigroups of nonzero regular elements of their transition semigroups is described. If the subshift is minimal, then this inverse limit is isomorphic, as a partial semigroup, to the -class associated to it in the free pro-aperiodic semigroup.
6 citations
TL;DR: In this article, the authors studied Δ-mixing and showed that a dynamical system is Δ-transitive if and only if it is Δmixing with respect to a thick set.
6 citations
TL;DR: In this article, the authors give a structure for a semigroup which is a semilattice of bisimple inverse semigroups, and characterize the idempotent separating congruences.
Abstract: The purpose of this paper is to give a structure for a semigroup which is a semilattice of bisimple inverse semigroups and satisfies certain conditions. For such a semigroup, we characterize the idempotent separating congruences.
6 citations
TL;DR: In this article, the authors define the radical of a semigroup S and investigate some of its properties, such as a quasi-regular two-sided ideal which contains each right ideal of the semigroup.
Abstract: In this paper we shall first define the radical of a semigroup S and investigate some of its properties. Just as in the case of rings, one finds that the radical of a semigroup is a quasi-regular two-sided ideal which contains each quasi-regular right ideal of the semigroup and that the radical of a semigroup contains each nil right ideal of the semigroup. If a semigroup with zero satisfies the minimum condition on left ideals and right ideals then its radical is also the left radical of the semigroup. One also finds that if S. is the semigroup of all row-monomial n x n matrices over S then the radical of S,, is the semigroup of all row-monomial n x n matrices over the radical of S. If T is a two-sided ideal of S then the radical of T is the intersection of T and the radical of S. In the latter part of the paper we shall study semisimple semigroups. If s, t E S, let spt provided that, if m is contained in some 0-transitive operand of S, then ms = mt. Thus p is a two-sided congruence called the radical congruence of S. If the radical congruence of S is the identity relation then S is semisimple. Since M is a 0-transitive operand of S if and only if M is a 0-transitive operand of S/p, then it is easily seen that S/p is semisimple. If S is semisimple and T is a two-sided ideal of S, then T is semisimple. Finally, if S contains more than one element, then S is semisimple if and only if S is isomorphic to a subdirect sum of a set of semigroups each of which has a faithful 0-transitive operand.
6 citations