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 paper, it was shown that a -simple strongly projective semigroup can be expressed by a Rees matrix semigroup over a left cancellative monoid and conversely, the result generalizes the classical theorem of Rees and amplifies the Rees theorem in semigroup given by Lallement and Petrich in 1969.
Abstract: A semigroup S is called rpp if all right principal ideals of S, regarded as S1-systems, are projective. An rpp semigroup S is said to be strongly rpp if for any a ∈ S, there exists a unique idempotent e such that and a = ea. In this paper, we show that a -simple strongly rpp semigroup can be expressed by a Rees matrix semigroup over a left cancellative monoid and conversely. Our result generalizes the classical theorem of Rees in 1940 and also amplifies the Rees theorem in semigroup given by Lallement and Petrich in 1969.
12 citations
TL;DR: In this paper, the authors studied connected components of open subsemigroups of semi-simple Lie groups by using control sets in the flag manifolds and their coverings, and showed that the union of all recurrent components is a semigroup.
Abstract: This paper studies connected components of open subsemigroups of non-compact semi-simple Lie groups by using control sets in the flag manifolds and their coverings. The concept of recurrent component is introduced and a method is given by which their number can be computed. It is shown that the union of all recurrent components is a semigroup. The idea of mid-reversibility comes up to show that an open semigroup has just one semigroup component if the identity belongs to its closure. A necessary and sufficient condition for mid-reversibility is proved showing that e.g. in a complex group any open semigroup is mid-reversible.
12 citations
12 citations
12 citations
TL;DR: A semigroup with an involution * is called a special involution semigroup if and only if, for every finite nonempty subset T of S, (3t G T)(Vu, v 6 T) tt* = uv' => u = v. as discussed by the authors.
Abstract: A semigroup 5 with an involution * is called a special involution semigroup if and only if, for every finite nonempty subset T of S, (3t G T)(Vu, v 6 T) tt* = uv' => u = v. It is shown that a semigroup is inverse if and only if it is a special involution semigroup in which every element invariant under the involution is periodic. Other examples of special involution semigroups are discussed; these include free semigroups, totally ordered cancellative commutative semigroups and certain semigroups of matrices. Some properties of the semigroup algebras of special involution semigroups are also derived. In particular, it is shown that their real and complex semigroup algebras are semiprimitive. 1. DEFINITIONS
12 citations