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Congruences on regular and completely regular semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

P. G. Trotter
P. G. Trotter
Affiliation:
University of Tasmania, Hobart, Tasmania, Australia
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Abstract

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Congruences on regular semigroups have been characterized in terms of normal equivalences on sets of idempotents and kernels of congruences. A revised characterization is presented here with considerably simplified expressions for the least and greatest congruences associated with normal equivalences and with a new description of kernels. The results are then applied to characterize congruences on completely regular semigroups.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 3 , June 1982 , pp. 388 - 398
Copyright
Copyright © Australian Mathematical Society 1982

References

Clifford, A. H. (1979), ‘Some questions on regular semigroups’, Symposium on regular semigroups, pp. 17–28, Northern Illinois University.Google Scholar
Clifford, A. H. and Preston, G. B. (1961 and 1967), The algebraic theory of semigroups, Mathematical Surveys 7, Vols. I and II, (Amer. Math. Soc., Providence, R.I.).Google Scholar
Ruth, Feigenbaum (1975), Kernels of regular semigroup homomorphisms, (Doctoral dissertation, University of South Carolina).Google Scholar
Ruth, Feigenbaum (1976), ‘Kernels of orthodox semigroup homomorphisms’, J. Austral. Math. Soc. Ser. A 22, 234–245.Google Scholar
Ruth, Feigenbaum (1979), ‘Regular semigroup congruences’, Semigroup Forum 17, 373–377.Google Scholar
Hall, T. E. (1972), ‘Congruences and Green's relations on regular semigroups’, Glasgow Math. J. 13, 167–175.CrossRefGoogle Scholar
Howie, J. M. (1976), An introduction to semigroup theory (Academic Press, London).Google Scholar
Nambooripad, K.S.S. (1974), ‘Structure of regular semigroups I’, Semigroup Forum 9, 354–363.Google Scholar
Petrich, M. (1978), ‘Congruences on inverse semigroups’, J. Algebra 55, 231–256.CrossRefGoogle Scholar
Thomas, L. Pirnot (1974), ‘Certain congruences on a completely regular semigroup’, Glasgow Math. J. 15, 109–120.Google Scholar
Reilly, N. R. and Scheiblich, H. E. (1967), ‘Congruences on regular semigroups’, Pacific J. Math. 23, 349–360.Google Scholar
Scheiblich, H. E. (1974), ‘Kernels of inverse semigroup homomorphisms’, J. Austral. Math. Soc. 18, 289–292.Google Scholar
Trotter, P. G. (1978), ‘Normal partitions of idempotents of regular semigroups’, J. Austral. Math. Soc. Ser. A 26, 110–114.Google Scholar