Characterizing pure, cryptic and Clifford inverse semigroups

Petrich, Mario. "Characterizing pure, cryptic and Clifford inverse semigroups." Czechoslovak Mathematical Journal 64.4 (2014): 1099-1112. <http://eudml.org/doc/269845>.

@article{Petrich2014,
abstract = {An inverse semigroup $S$ is pure if $e=e^2$, $a\in S$, $e<a$ implies $a^2=a$; it is cryptic if Green’s relation $\mathcal \{H\}$ on $S$ is a congruence; it is a Clifford semigroup if it is a semillatice of groups. We characterize the pure ones by the absence of certain subsemigroups and a homomorphism from a concrete semigroup, and determine minimal nonpure varieties. Next we characterize the cryptic ones in terms of their group elements and also by a homomorphism of a semigroup constructed in the paper. We also characterize groups and Clifford semigroups in a similar way by means of divisors. The paper also contains characterizations of completely semisimple inverse and of combinatorial inverse semigroups in a similar manner. It ends with a description of minimal non-$\mathcal \{V\}$ varieties, for varieties $\mathcal \{V\}$ of inverse semigroups considered.},
author = {Petrich, Mario},
journal = {Czechoslovak Mathematical Journal},
keywords = {inverse semigroup; pure inverse semigroup; cryptic inverse semigroup; Clifford semigroup; group-closed inverse semigroup; pure variety; completely semisimple inverse semigroup; combinatorial inverse semigroup; variety; pure inverse semigroups; cryptic inverse semigroups; Clifford semigroups; semisimple semigroups; combinatorial semigroups; lattices of varieties of inverse semigroups},
language = {eng},
number = {4},
pages = {1099-1112},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterizing pure, cryptic and Clifford inverse semigroups},
url = {http://eudml.org/doc/269845},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Petrich, Mario
TI - Characterizing pure, cryptic and Clifford inverse semigroups
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 1099
EP - 1112
AB - An inverse semigroup $S$ is pure if $e=e^2$, $a\in S$, $e<a$ implies $a^2=a$; it is cryptic if Green’s relation $\mathcal {H}$ on $S$ is a congruence; it is a Clifford semigroup if it is a semillatice of groups. We characterize the pure ones by the absence of certain subsemigroups and a homomorphism from a concrete semigroup, and determine minimal nonpure varieties. Next we characterize the cryptic ones in terms of their group elements and also by a homomorphism of a semigroup constructed in the paper. We also characterize groups and Clifford semigroups in a similar way by means of divisors. The paper also contains characterizations of completely semisimple inverse and of combinatorial inverse semigroups in a similar manner. It ends with a description of minimal non-$\mathcal {V}$ varieties, for varieties $\mathcal {V}$ of inverse semigroups considered.
LA - eng
KW - inverse semigroup; pure inverse semigroup; cryptic inverse semigroup; Clifford semigroup; group-closed inverse semigroup; pure variety; completely semisimple inverse semigroup; combinatorial inverse semigroup; variety; pure inverse semigroups; cryptic inverse semigroups; Clifford semigroups; semisimple semigroups; combinatorial semigroups; lattices of varieties of inverse semigroups
UR - http://eudml.org/doc/269845
ER -