Semigroup Forum

, Volume 68, Issue 2, pp 202–208 | Cite as

The Structure of Commutative Semigroups with the Ideal Retraction Property

Research Article
First Online:
Received:

Abstract

A semigroup is said to have the ideal retraction property when each of its ideals is a homomorphic retraction of the whole semigroup. This paper presents a complete characterization of the commutative semigroups that enjoy this property. The fundamental building blocks of these semigroups are the 2-cores and the semilattice of idempotents. Structure for semilattices with the ideal retraction property was discussed in an earlier paper and the structure of the 2-core is described in detail within this paper.

Keywords

Building Block Early Paper Complete Characterization Commutative Semigroup Ideal Retraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • K. D. Aucoin
    • 1
  • J. A. Dumesnil
    • 2
  • J. A. Hildebrant
    • 3
  1. 1. Department of Mathematics, McNeese State University, Lake Charles, LA 70609 USA
  2. 2.Stephen F. Austin State University Nacogdoches, Texas 75962USA
  3. 3.Louisiana State University Baton Rouge, LA 70803USA

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