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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
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Abstract

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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

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[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