Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-17T05:06:41.325Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalised retract semigroups

Published online by Cambridge University Press:  17 April 2009

Karl Auinger
Karl Auinger
Affiliation:
Institut für Mathematik, Strudlhofgasse 4, A-1090 Wien, Austria
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a description of the structure of the semigroups for which each principal ideal is a retract. The globally idempotent case is solved quickly using a—suitably modified—construction which has been developed by Tully for the study of semigroups in which each ideal is a retract. The general case can be treated by a naturally obtained semigroup of subsets of the semigroup constructed for the globally idempotent case.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 3 , June 1991 , pp. 499 - 508
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Auinger, K., ‘Semigroups with complemented congruence lattices’, Algebra Universalis 22 (1986), 192–204.CrossRefGoogle Scholar
[2]Auinger, K., ‘Weakly reductive semigroups with atomistic congruence lattices’, J. Austral. Math. Soc. (Series A) 49 (1990), 59–71.CrossRefGoogle Scholar
[3]Lallement, G. and Petrich, M., ‘Structure d'une classe de demi-groupes réguliers’, J. Math. Pures Appl. 48 (1969), 345–397.Google Scholar
[4]Tully, E.G. Jr., ‘Semigroups in which each ideal is a retract’, J. Austral. Math. Soc. 9 (1969), 239–245.CrossRefGoogle Scholar