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Right inverse semigroups

  • S. Madhavan (a1)

Abstract

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.

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References

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Bailes, G. L., (1972), Right inverse semigroups, Doctoral dissertation, Clemson University.
Clifford, A. H. and Preston, G. B. (1961), The algebraic theory of semigroups, Vol. I (Maths. Surveys No. 7, Amer. Math. Soc., Providence, R.I.).
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