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Right inverse semigroups

Published online by Cambridge University Press:  09 April 2009

S. Madhavan
S. Madhavan
Affiliation:
Department of Mathematics University CollegeTrivandrum—695 001 Kerala State, India
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Abstract

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In a recent paper of the author the well-known Vagner-Preston Theorem on inverse semigroups was generalized to include a wider class of semigroups, namely right normal right inverse semigroups. In an attempt to generalize the theorem to include all right inverse semigroups, the notion of μ – μi transformations is introduced in the present paper. It is possible to construct a right inverse band BM(X) of μ – μi transformations. From this a set AM(X) for which left and right units are in BM(X) and satisfying certain conditions is constructed. The semigroup AM(X) so constructed is a right inverse semigroup. Conversely every right inverse semigroup can be isomorphically embedded in a right inverse semigroup constructed in this way.

1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 20.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 3 , May 1980 , pp. 322 - 330
Copyright
Copyright © Australian Mathematical Society 1980

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