Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
Papers published on a yearly basis
Papers
More filters
28 Oct 2015
TL;DR: In this article, it was shown that a cancellative semigroup admitting conjugates is embeddable in a nilpotent group of class 2 if and only if it satisfies the conjugacy law x^y^z = X^y.
Abstract: We prove conjugate analogs of Mal’cev-Neumann-Taylor-Levi’s theorems. In other words, we characterize semigroups em- beddable in nilpotent groups of class n by means of conjugacy laws involving semigroup laws described by Mal’cev, Neumann and Taylor. Moreover we prove that a cancellative semigroup admitting conjugates is embeddable in a nilpotent group of class 2 if and only if it satisfies the conjugacy law x^y^z = x^y. Also adapting Ore’s techniques we describe an exact procedure for embedding a cancellative semigroup admitting conjugates into a group.
1 citations
Posted Content•
TL;DR: In this article, a linear control system π on a connected Lie group G is considered, where the accessibility set A from the identity e is in general not a semigroup.
Abstract: Let us consider a linear control system \Sigma on a connected Lie group G. It is known that the accessibility set A from the identity e is in general not a semigroup. In this article we associate a new algebraic object S to \Sigma which turns out to be a semigroup, allowing the use of the semigroup machinery to approach \Sigma. In particular, we obtain some controllability results.
1 citations
TL;DR: This paper constructs for a given algebra automaton the semigroup of functions which can be defined by that algebra Automaton as an operator semigroup with prescribed generators and characterize the algebra automata of algebras in a particular variety.
1 citations
TL;DR: In this article, it was shown that for any set A of metric semigroups there exists a metric semigroup U such that each S in A is topologically isomorphic to a subsemigroup of U.
Abstract: J.H. Michael recently proved that there exists a metric semigroup U such that every compact metric semigroup with property P is topologically isomorphic to a subsemigroup of U ; where a semigroup S has property P if and only if for each x, y in S , x ≠ y , there is a z in S such that xs ≠ yz or zx ≠ zy A stronger result is proved here more simply. It is shown that for any set A of metric semigroups there exists a metric semigroup U such that each S in A is topologically isomorphic to a subsemigroup of U . In particular this is the case when A is the class of all separable metric semigroups, or more particularly the class of all compact metric semigroups.
1 citations
TL;DR: In this paper, the authors give a full description of the semilattice of group congruences on an arbitrary eventually regular (orthodox) semigroup and investigate UBG-congruences on such an eventually regular semigroup.
Abstract: A semigroup is called eventually regular if each of its elements has a regular power. In this paper we study certain fundamental congruences on an eventually regular semigroup. We generalize some results of Howie and Lallement (1966) and LaTorre (1983). In particular, we give a full description of the semilattice of group congruences (together with the least such a congruence) on an arbitrary eventually regular (orthodox) semigroup. Moreover, we investigate UBG-congruences on an eventually regular semigroup. Finally, we study the eventually regular subdirect products of an E-unitary semigroup and a Clifford semigroup.
1 citations