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The semidirect product of an inverse semigroup and a group

Published online by Cambridge University Press:  17 April 2009

G. B. Preston
G. B. Preston
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168.
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Abstract

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It is shown that a semidirect product of an inverse semigroup and a group, in that order, contains an inverse subsemigroup that is a retract and that, together with the retraction mapping, forms free inverse morphic image of the semidirect product. The congruence determined by the retraction mapping is shown to be determined by the semigroup of idempotents of the semidirect product.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 2 , April 1986 , pp. 261 - 272
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Clifford, A. H. and Preston, G. B., “The algebraic theory of semigroups, Vol. 2”, Math. Surveys, No. 7, Amer. Math. Soc. 1967.CrossRefGoogle Scholar
[2]Nico, W. R., “On the regularity of semidirect products”, J. of Algebra 80 (1983), 29–36.Google Scholar
[3]Preston, G. B., “Semidirect products of semigroups”, Proc. Royal Society of Edinburgh (to appear).Google Scholar