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On right self-injective regular semigroups, II

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Kunitaka Shoji
Kunitaka Shoji
Affiliation:
Department of Mathematics Shimane UniversityMatsue, Shimane, Japan
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Abstract

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It is shown that a semigroup is right self-injective and a band of groups if and only if it is isomorphic to the spined product of a self-injective semilattice of groups and a right self-injective band. A necessary and sufficient condition for a band to be right self-injective is given. It is shown that a left [right] self-injective semigroup has the [anti-] representation extension property and the right [left] congruence extension property.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 2 , April 1983 , pp. 182 - 198
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. 1 (Math. Surveys, No 7, Amer. Math. Soc., Providence, R.I., 1961).Google Scholar
[2]Hall, T. E., ‘On regular semigroups whose idempotents form a subsemigroup’, Bull. Austral. Math. Soc. 1 (1969), 195–208.CrossRefGoogle Scholar
[3]Hall, T. E., ‘Almost commutative bands’, Glasgow Math. J. 13 (1972), 176–178.CrossRefGoogle Scholar
[4]Hall, T. E., ‘Representation extension and amalgamation for semigroups’, Quart. J. Math. Oxford Ser. 29 (1978), 309–334.CrossRefGoogle Scholar
[5]Hall, T. E., ‘Epimorphisms and dominions’, Semigroup Forum 24 (1982), 271–283.CrossRefGoogle Scholar
[6]Kimura, N., ‘The structure of idempotent semigroups. (I)’, Pacific J. Math. 8 (1958), 257–275.CrossRefGoogle Scholar
[7]Schein, B. M., ‘Injective monars over inverse semigroups’, Algebraic theory of semigroups, pp. 519–544 (Colloquia Math. Soc. Janos Bolyai 20, Szeged (Hungary), 1976).Google Scholar
[8]Shoji, K., ‘Injective hulls of certain right reductive semigroups S as right S-systems’, Mem. Fac. Sci. Shimane Univ. 14 (1980), 25–34.Google Scholar
[9]Shoji, K., ‘Right self-injective semigroups are absolutely closed’, Mem. Fac. Sci. Shimane Univ. 14 (1980), 35–39.Google Scholar
[10]Shoji, K., ‘On right self-injective regular semigroups’, Semigroup Forum 25 (1982), 51–71.CrossRefGoogle Scholar
[11]Yamada, M., ‘Strictly inversive semigroups’, Sci. Rep. Shimane Univ. 13 (1964), 128–138.Google Scholar
[12]Yamada, M., ‘On a regular semigroup in which the idempotents form a band’, Pacific J. Math. 33 (1970), 261–272.CrossRefGoogle Scholar