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Rees matrix covers for a class of abundant semigroups

Published online by Cambridge University Press:  14 November 2011

Mark V. Lawson
Mark V. Lawson
Affiliation:
Lincoln College, Oxford OX1 3DR, U.K
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Synopsis

Recently considerable attention has been paid to the study of locally inverse regular semigroups. McAlister [14] obtained a description of such semigroups as locally isomorphic images of regular Rees matrix semigroups over an inverse semigroup. The class of abundant semigroups originally arose from ‘homological’ considerations in the theory of S-systems: they are the semigroup theoretic analogue of PP-rings. Cancellative monoids, full subsemigroups of regular semigroups as well as the multiplicative semigroups of PP rings are abundant. The aim of this paper is to show how the structure theory described above for regular semigroups may be generalised to a class of abundant semigroups.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 1-2 , 1987 , pp. 109 - 120
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Armstrong, S.. The structure of type A semigroups. Semigroup Forum 29 (1984), 319–336.Google Scholar
2El-Qallali, A.., L*-unipotent semigroups (preprint).Google Scholar
3El-Qallali, A. and Fountain, J. B.. Idempotent connected abundant semigroups. Proc. Roy. Soc. Edinburgh Sect. A 91 (1981), 79–90.Google Scholar
4El-Qallali, A. and Fountain, J. B.. Quasi-adequate semigroups. Proc. Roy. Soc. Edinburgh Sect. A 91 (1981), 91–99.Google Scholar
5Fountain, J. B.. Adequate semigroups. Proc. Edinburgh Math. Soc. (2) 22 (1979), 113–125.Google Scholar
6Fountain, J. B.. Abundant semigroups. Proc. London Math. Soc. (3) XLIV (1982), 103–129.Google Scholar
7Hall, T. E.. Some properties of local subsemigroups inherited by larger subsemigroups. Semigroup Forum 25 (1982), 35–49.Google Scholar
8Howie, J. M.. An Introduction to Semigroup Theory (London: Academic Press, 1976).Google Scholar
9Lawson, M. V.. The structure of type A semigroups. Quart. J. Math. Oxford Ser. (2) 37 (1986), 279–298.CrossRefGoogle Scholar
10Lawson, M. V.. Abundant Rees matrix semigroups. J. Austral. Math. Soc. Ser. A 42 (1987), 132–142.Google Scholar
11Lawson, M. V.. The natural partial order on an abundant semigroup. Proc. Edinburgh Math. Soc. 30 (1987), 169–186.Google Scholar
12Lawson, M. V.. Semigroups and ordered categories (preprint).Google Scholar
13McAlister, D. B.. Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups. J. Austral. Math. Soc. Ser. A 31 (1981), 325–336.CrossRefGoogle Scholar
14McAlister, D. B.. Rees matrix covers for locally inverse semigroups. Trans. Amer. Math. Soc. 277 (1983), 727–738.CrossRefGoogle Scholar
15Nambooripad, K. S. S.. Structure of regular semigroups I. Mem. Amer. Math. Soc. 22 (224) (1970).Google Scholar
16Nambooripad, K. S. S.. The natural partial order on a regular semigroup. Proc. Edinburgh Math. Soc. (2) 23 (1980), 249–260.Google Scholar
17Palmer, A.. Proper right type A semigroups (M.Phil Thesis, York University, 1982.)Google Scholar