Normal cryptogroups with an associate subgroup

Title:

Normal cryptogroups with an associate subgroup

Creator:

Petrich, Mario

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7085bb3f-3463-4f04-b648-c19ed4c43e01
uuid:7085bb3f-3463-4f04-b648-c19ed4c43e01

Subject:

semigroup, normal cryptogroup, associate subgroup, representation, strong semilattice of semigroups, and Rees matrix semigroup

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $S$ be a semigroup. For $a,x\in S$ such that $a=axa$, we say that $x$ is an associate of $a$. A subgroup $G$ of $S$ which contains exactly one associate of each element of $S$ is called an associate subgroup of $S$. It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup $S$ is a completely regular semigroup whose $\mathcal H$-relation is a congruence and $S/\mathcal H$ is a normal band. Using the representation of $S$ as a strong semilattice of Rees matrix semigroups, in a previous communication we characterized those that have an associate subgroup. In this paper, we use that result to find three more representations of this semigroup. The main one has a form akin to the one of semigroups in which the identity element of the associate subgroup is medial.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

289-305

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:2

Harvested from:

CDK

Metadata only:

false