Semigroups with good and bad magnifiers

JOURNAL OF ALGEBRA

卷:267

Article

Gutan, M ; Kisielewicz, A

关键词: semigroup;    magnifier;    string rewriting;    presentation;    normal form;   

DOI  :  10.1016/S0021-8693(03)00396-X

来源: Elsevier

【 摘 要 】

An element a of a semigroup S is called a (left) magnifier if there exists a proper subset M of S such that aM = S. If there is a minimal subset M with this property that is a right ideal of S, then the magnifier a is called very good. If such a minimal subset is a subsemigroup of S, then a is called good. Otherwise, it is called bad. It is well known that if a semigroup S has a very good magnifier, then all magnifiers in S are very good. A long-standing open problem is whether there exist semigroups having both good and bad magnifiers. In this paper we answer this question in positive and prove several results concerning such semigroups. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

Free