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Abundant Rees matrix semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

M. V. Lawson
M. V. Lawson
Affiliation:
Department of Mathematics, University of York, Heslington, York, United Kingdom
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Abstract

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The class of abundant semigroups originally arose from ‘homological’ considerations in the theory of S-systems: they are the semigroup theoretic counterparts of PP-rings. Cancellative monoids, full subsemigroups of regular semigroups as well as the multiplicative semigroups of PP-rings are abundant. In this paper we investigate the properties of Rees matrix semigroups over abundant semigroups. Some of our results generalise McAlister's work on regular Rees matrix semigroups.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 1 , February 1987 , pp. 132 - 142
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Armstrong, S., ‘The structure of type A semigroups’, Semigroup Forum 29 (1984), 319–336.CrossRefGoogle Scholar
[2]El-Qallali, A. and Fountain, J. B., ‘Idempotent connected abundant semigroups’, Proc. Roy. Soc. Edinburgh Sect. A91 (1981), 79–90.CrossRefGoogle Scholar
[3]Fountain, J. B., ‘Adequate semigroups’, Proc. Edinburgh Math. Soc. 22 (1979), 113–125.CrossRefGoogle Scholar
[4]Fountain, J. B., ‘Abundant semigroups’, Proc. London Math. Soc. (3) 44 (1982), 103–129.CrossRefGoogle Scholar
[5]Hall, T. E., ‘On regular semigroups’, J. Algebra 24 (1973), 1–24.CrossRefGoogle Scholar
[6]Howie, J. M., An Introduction to Semigroup Theory (Academic Press, London, 1976).Google Scholar
[7]Lawson, M. V., ‘The structure of type A semigroups’, Quart. J. Math., to appear.Google Scholar
[8]Lawson, M. V., ‘The natural partial order on an abundant semigroup’ Proc. Edinburgh Math. Soc., to appear.Google Scholar
[9]Ljapin, E. S., Semigroups (Amer. Math. Soc., revised edition, 1968).Google Scholar
[10]McAlister, D. B., ‘Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups’ J. Austral. Math. Soc. (Series A) 31 (1981), 325–336.CrossRefGoogle Scholar
[11]Meakin, J., ‘The Rees construction in regular semigroups’, preprint.Google Scholar
[12]Nambooripad, K. S. S., ‘Structure of regular semigroups I’ Mem. Amer. Math. Soc. 22 Number 224 (1979).Google Scholar