Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-15T02:31:38.884Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

Bailes, G. L., (1972), Right inverse semigroups, Doctoral dissertation, Clemson University.Google Scholar
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.).Google Scholar
Ewing, E. W. (1971), Contribution to the study of regular semigroups, Doctoral dissertation, University of Kentucky.Google Scholar
Hall, E. (1969), ‘On regular semigroups whose idempotents form a subsemigroups, Bull. Australian Math. Soc. 1, 195–208.CrossRefGoogle Scholar
Madhavan, S. (1976), ‘On right normal right inverse semigroups’, Semigroup Forum 12, 333–339.CrossRefGoogle Scholar
Srinivasan, B. R. (1968), ‘Weakly inverse semigroups’, Math. Annalen 176, 324–333.CrossRefGoogle Scholar
Venkatesan, P. S. (1972), ‘Bisimple left inverse semigroups’, Semigroup Forum 4, 34–35.CrossRefGoogle Scholar
Warne, R. J. (1980), ℒ-Unipotent semigroups’, Nigerian J. Sci., to appear.Google Scholar
Yamada, Miyuki (1967), ‘Regular semigroups whose idempotents satisfy permutation identities’, Pac. J. Math. 21, 371–392.CrossRefGoogle Scholar