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Morita equivalence for semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

S. Talwar
S. Talwar
Affiliation:
Department of Mathematics, University of York, Heslington, York Y01 5DD
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Abstract

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In this paper we shall extend the classical theory of Morita equivalence to semigroups with local units. We shall use the concept of a Morita context to rediscover the Rees theorem and to characterise completely 0-simple and regular bisimple semigroups.

MSC classification

Secondary: 20M50: Connections of semigroups with homological algebra and category theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 1 , August 1995 , pp. 81 - 111
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Abrams, G. D. (1983), ‘Morita equivalence for rings with local units’, Comm. Algebra, 11, 801–837.CrossRefGoogle Scholar
[2]Allen, D. (1991), ‘A structure theory for finite regular semigroups’, in: Monoids and Semigroups with Applications (ed. Rhodes, J.) (World Scientific, Singapore) pp. 403–423.Google Scholar
[3]Anderson, F. W. and Fuller, K. R. (1974), Rings and categories of modules, Graduate Texts in Mathematics 13 (Springer, Berlin).CrossRefGoogle Scholar
[4]Anh, P. N. and Marki, L. (1987), ‘Morita equivalence for rings without identity’, Tsukuba J. Math. 11, 1–16.Google Scholar
[5]Banaschewski, B. (1972), ‘Functors into the category of M-sets’, Abh. Math. Sem. Univ. Hamburg 8, 49–64.CrossRefGoogle Scholar
[6]Barga, J. M. and G-Rodeja F, E. (1980), ‘Morita equivalence of monoids’, Semigroup Forum 19, 101–106.CrossRefGoogle Scholar
[7]Byleen, K., Meakin, J. and Pastijn, F. (1978), ‘The fundamental four spiral semigroup’, J. Algebra 54, 6–26.CrossRefGoogle Scholar
[8]Hotzel, E. (1976), ‘Dual D-operands and the Rees Theorem’, in: Algebraic theory of semigroups, Colloq. Math. Soc. János Bolyai 20.Google Scholar
[9]Howie, J. M. (1976), An introduction to semigroup theory (Academic Press, London).Google Scholar
[10]Jacobson, N. (1980), Basic Algebra 2 (Freeman, San Francisco).Google Scholar
[11]Knauer, U. (1972), ‘Projectivity of acts and morita equivalence of monoids’, Semigroup Forum 3, 359–370.CrossRefGoogle Scholar
[12]Knauer, U. and Normak, P. (1990), ‘Mortita duality of monoids’, Semigroup Forum 40, 39–57.CrossRefGoogle Scholar
[13]Mitchell, B. (1965), Theory of categories (Academic Press, London).Google Scholar
[14]Morita, K. (1961), ‘Category-isomorphism and endomorphism rings of modules’, Trans. Amer. Math. Soc. 103, 451–469.CrossRefGoogle Scholar
[15]Rees, D. (1940), ‘On semi-groups’, Proc. Cambridge Phil. Soc. 36, 387–400.CrossRefGoogle Scholar