Idempotent Separating Congruences on an Orthodox Semigroup
Publications de l'Institut Mathématique, _N_S_53 (1993) no. 67, p. 45
Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
The least inverse congruence $Y$ on an orthodox semigroup
$S$ was considered by Yamada [14] for the case where the band of
idempotents of $S$ is normal. It was considered in the general orthodox
case by Schein [12] and Hall [4]. An explicit construction for
idempotent separating congruences on an orthodox semigroup $S$ in terms
of idempotent separating congruences on $S/Y$ was given by McAlister
[8]. In this paper we describe these congruences by inverse congruences
contained in $\mu\circ Y$, where $\mu$ is the greatest idempotent
separating congruence on $S$. Also, we obtain some mutually inverse
complete lattice isomorphisms of intervals $[Y,\mu \circ Y]$ and
$[\varepsilon,\mu]$, where $\varepsilon$ is the identity relation on
$S$.
Classification :
20M19
@article{PIM_1993_N_S_53_67_a5,
author = {Dragica N. Krgovi\'c},
title = {Idempotent {Separating} {Congruences} on an {Orthodox} {Semigroup}},
journal = {Publications de l'Institut Math\'ematique},
pages = {45 },
year = {1993},
volume = {_N_S_53},
number = {67},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1993_N_S_53_67_a5/}
}
Dragica N. Krgović. Idempotent Separating Congruences on an Orthodox Semigroup. Publications de l'Institut Mathématique, _N_S_53 (1993) no. 67, p. 45 . http://geodesic.mathdoc.fr/item/PIM_1993_N_S_53_67_a5/