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Rees matrix semigroups

Published online by Cambridge University Press:  20 January 2009

Mark V. Lawson
Mark V. Lawson
Affiliation:
Fachbereich Mathematik AG5, Technische Hochschule, D-6100, Darmstadt, Schlossgartenstr 7, West Germany
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Abstract

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In this paper we provide a new, abstract characterisation of classical Rees matrix semigroups over monoids with zero. The corresponding abstract class of semigroups is obtained by abstracting a number of algebraic properties from completely 0-simple semigroups: in particular, the relationship between arbitrary elements and idempotents.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 1 , February 1990 , pp. 23 - 37
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

REFERENCES

1.Asibong-Ibe, U., The structure of type A ω-semigroups (D.Phil. Thesis, York, 1981).Google Scholar
2.De Barros, C. M., Sur les catégories ordonnés régulières, Cahiers Topologie Géom. Différentielle Catégoriques 11 (1969), 23–55.Google Scholar
3.Batbedat, A. and Reilly, N. R., Categories and biunary semigroups, Simon Stevin 56 (1982), 181–209.Google Scholar
4.El-Qallali, A., Structure theory for abundant and related semigroups (D.Phil. Thesis, York, 1980).Google Scholar
5.Fountain, J. B., Abundant semigroups, Proc. London Math. Soc. (3) 44 (1982), 103–129.CrossRefGoogle Scholar
6.Howie, J. M., An Introduction to the Theory of Semigroups (Academic Press, London, 1976).Google Scholar
7.Lallement, G. and Petrich, M., Décompositions I-matricielles d'un demi-groupe, J. Math. Pures Appl. 45 (1966), 67–117.Google Scholar
8.Lallement, G. and Petrich, M., A generalisation of the Rees theorem in semigroups, Acta. Sci. Math. (Szeged) 30 (1969), 113–132.Google Scholar
9.Lawson, M. V., Abundant Rees matrix semigroups, J. Austral. Math. Soc. Ser. A 42 (1987), 132–142.CrossRefGoogle Scholar
10.Lawson, M. V., Primitive U-semiabundant semigroups, in preparation.Google Scholar
11.Lawson, M. V., Semigroups and ordered categories I, submitted.Google Scholar
12.Lawson, M. V., Semigroups and ordered categories II, in preparation.Google Scholar
13.Marki, L., On locally regular Rees matrix semigroups, Acta. Sci. Math. (Szeged) 37 (1975), 95–102.Google Scholar
14.Meakin, J., The Rees construction in regular semigroups, Colloq. Math. Soc. János Bolyai 39 (1981), 115–156.Google Scholar
15.Rees, D., On semi-groups, Proc. Cambridge Philos. Soc. 36 (1940), 387–400.CrossRefGoogle Scholar
16.Steinfeld, O., On a generalisation of completely 0-simple semigroups, Acta. Sci. Math. (Szeged) 28 (1967), 135–145.Google Scholar
17.Suschkewitsch, A., Über die endlichen Gruppen ohne das Gesetz der eindeutigen Umkehrbarkeit, Math. Ann. 99 (1928), 30–50.CrossRefGoogle Scholar