REGULAR CONGRUENCES ON AN IDEMPOTENT-REGULAR-SURJECTIVE SEMIGROUP.
In: Bulletin of the Australian Mathematical Society, Jg. 88 (2013-10-01), Heft 2, S. 190-196
Online
academicJournal
Zugriff:
A semigroup $S$ is called idempotent-surjective (respectively, regular-surjective) if whenever $\rho $ is a congruence on $S$ and $a\rho $ is idempotent (respectively, regular) in $S/ \rho $, then there is $e\in {E}_{S} \cap a\rho $ (respectively, $r\in \mathrm{Reg} (S)\cap a\rho $), where ${E}_{S} $ (respectively, $\mathrm{Reg} (S)$) denotes the set of all idempotents (respectively, regular elements) of $S$. Moreover, a semigroup $S$ is said to be idempotent-regular-surjective if it is both idempotent-surjective and regular-surjective. We show that any regular congruence on an idempotent-regular-surjective (respectively, regular-surjective) semigroup is uniquely determined by its kernel and trace (respectively, the set of equivalence classes containing idempotents). Finally, we prove that all structurally regular semigroups are idempotent-regular-surjective. [ABSTRACT FROM AUTHOR]
Titel: |
REGULAR CONGRUENCES ON AN IDEMPOTENT-REGULAR-SURJECTIVE SEMIGROUP.
|
---|---|
Autor/in / Beteiligte Person: | GIGOŃ, ROMAN S. |
Link: | |
Zeitschrift: | Bulletin of the Australian Mathematical Society, Jg. 88 (2013-10-01), Heft 2, S. 190-196 |
Veröffentlichung: | 2013 |
Medientyp: | academicJournal |
ISSN: | 0004-9727 (print) |
DOI: | 10.1017/S0004972713000270 |
Schlagwort: |
|
Sonstiges: |
|