Normal cryptogroups with an associate subgroup

Petrich, Mario. "Normal cryptogroups with an associate subgroup." Czechoslovak Mathematical Journal 63.2 (2013): 289-305. <http://eudml.org/doc/260669>.

@article{Petrich2013,
abstract = {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.},
author = {Petrich, Mario},
journal = {Czechoslovak Mathematical Journal},
keywords = {semigroup; normal cryptogroup; associate subgroup; representation; strong semilattice of semigroups; Rees matrix semigroup; normal cryptogroups; associate subgroups; strong semilattices of semigroups; Rees matrix semigroups; completely regular semigroups; normal cryptogroups; normal bands of groups},
language = {eng},
number = {2},
pages = {289-305},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Normal cryptogroups with an associate subgroup},
url = {http://eudml.org/doc/260669},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Petrich, Mario
TI - Normal cryptogroups with an associate subgroup
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 289
EP - 305
AB - 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.
LA - eng
KW - semigroup; normal cryptogroup; associate subgroup; representation; strong semilattice of semigroups; Rees matrix semigroup; normal cryptogroups; associate subgroups; strong semilattices of semigroups; Rees matrix semigroups; completely regular semigroups; normal cryptogroups; normal bands of groups
UR - http://eudml.org/doc/260669
ER -