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Congruences on Orthodox Semigroups

Published online by Cambridge University Press:  09 April 2009

John Meakin
John Meakin
Affiliation:
Monash University Clayton, Victoria
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A semigroup S is called regular if a ∈ aSa for every element a in S. The elementary properties of regular semigroups may be found in A. H. Clifford and G. B. Preston [1]. A semigroup S is called orthodox if S is regular and if the idempotents of S form a subsemigroup of S.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 3 , August 1971 , pp. 323 - 341
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, volume I (Math. Surveys, number 7, Amer. Math. Soc. 1961).Google Scholar
[2]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, volume II (Math. Surveys, number 7, Amer. Math. Soc. 1967).CrossRefGoogle Scholar
[3]Hall, T. E., ‘On regular semigroups whose idempotents form a subsemigroup’, Bull. Australian Math. Soc. 1, (1969).CrossRefGoogle Scholar
[4]Howie, J. M., ‘The maximum idempotent-separating congruence on an inverse semigroup’. Proc. Edinburgh Math. Soc. (2) 14 (1964/1965), 71–79.CrossRefGoogle Scholar
[5]Lallement, G., ‘Demi-groupes réguliers’, Annali Di. Math., 1967 Tone 77.CrossRefGoogle Scholar
[6]Preston, G. B., ‘Inverse semigroups’. J. London Math. Soc. 29 (1954), 396–403.CrossRefGoogle Scholar
[7]Preston, G. B., ‘The structure of normal inverse semigroups’, Proc. Glasgow Math. Assoc. 3 (1956), 1–9.Google Scholar
[8]Reilly, N. R. and Scheiblich, H. E., ‘Congruences on regular semigroups’, Pacific J. of Mathematics 23 (1967), 349–360.CrossRefGoogle Scholar
[9]Yamada, M., ‘Regular semigroups whose idempotents satisfy permutation identities’, Pacific J. of Mathematics, (2) 21 (1967), 371–392.Google Scholar