Hostname: page-component-7c8c6479df-ph5wq Total loading time: 0 Render date: 2024-03-28T09:02:56.185Z Has data issue: false hasContentIssue false

Morita equivalence for semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

S. Talwar
Affiliation:
Department of Mathematics, University of York, Heslington, York Y01 5DD
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Abrams, G. D. (1983), ‘Morita equivalence for rings with local units’, Comm. Algebra, 11, 801837.Google 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. 403423.Google Scholar
[3]Anderson, F. W. and Fuller, K. R. (1974), Rings and categories of modules, Graduate Texts in Mathematics 13 (Springer, Berlin).Google Scholar
[4]Anh, P. N. and Marki, L. (1987), ‘Morita equivalence for rings without identity’, Tsukuba J. Math. 11, 116.Google Scholar
[5]Banaschewski, B. (1972), ‘Functors into the category of M-sets’, Abh. Math. Sem. Univ. Hamburg 8, 4964.Google Scholar
[6]Barga, J. M. and G-Rodeja F, E. (1980), ‘Morita equivalence of monoids’, Semigroup Forum 19, 101106.Google Scholar
[7]Byleen, K., Meakin, J. and Pastijn, F. (1978), ‘The fundamental four spiral semigroup’, J. Algebra 54, 626.Google 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, 359370.Google Scholar
[12]Knauer, U. and Normak, P. (1990), ‘Mortita duality of monoids’, Semigroup Forum 40, 3957.Google 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, 451469.Google Scholar
[15]Rees, D. (1940), ‘On semi-groups’, Proc. Cambridge Phil. Soc. 36, 387400.Google Scholar