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On the foundations of inverse monoids and inverse algebras

Published online by Cambridge University Press:  20 January 2009

Jonathan Leech
Jonathan Leech
Affiliation:
Department of Mathematics, Westmont College, 955 La Paz Road, Santa Barbara, California 93108–1099, U.S.A. E-mail address: [email protected]
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Abstract

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Symmetric inverse monoids of objects in arbitrary categories are studied. Necessary and sufficient conditions are given for such monoids to be E-unitary or else form (complete) inverse algebras. Particular attention is given to symmetric inverse monoids of objects in free categories.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 1 , February 1998 , pp. 1 - 21
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

REFERENCES

1.Ademek, J., Herrlich, H. and Strecker, G. E., Abstract and Concrete Categories (Wiley Interscience, New York, 1990).Google Scholar
2.Barr, M. and Wells, C., Toposes, Triples and Theories (Springer-Verlag, New York, 1985).CrossRefGoogle Scholar
3.Clifford, A. H., A class of d-simple semigroups, Amer. J. Math. 15 (1953), 541–556.Google Scholar
4.Gaifman, H., Infinite Boolean polynomials, I, Fund. Math. 54 (1964), 229–250.CrossRefGoogle Scholar
5.Grillet, P. A., Semigroups, An Introduction to the Structure Theory (Marcel Dekker, New York, 1995).Google Scholar
6.Hales, A. W., On the non-existence of free complete Boolean algebras, Fund. Math. 54 (1964), 45–66.CrossRefGoogle Scholar
7.Howie, J. M., An Introduction to Semigroup Theory (Academic Press, London, 1976).Google Scholar
8.Johns-Tone, P. T., Stone Spaces (Cambridge University Press, Cambridge, 1982).Google Scholar
9.Kochin, B. P., The structure of inverse ideal-simple ω-semigroups, Vestnik Leningrad. Univ. 23 (1968), 41–50 (in Russian).Google Scholar
10.Lawson, M. V., The geometric theory of inverse semigroups, I, J. Pure Appl. Algebra 67 (1990), 151–177.CrossRefGoogle Scholar
11.Leech, J. E., The D-category of a monoid, Semigroup Forum 34 (1986), 89–116.CrossRefGoogle Scholar
12.Leech, J. E., Constructing inverse monoids from small categories, Semigroup Forum 36 (1987), 89–116.CrossRefGoogle Scholar
13.Leech, J. E., Inverse monoids with a natural semilattice ordering, Proc. London Math. Soc. (3) 70 (1995), 146–182.CrossRefGoogle Scholar
14.Munn, W. D., Regular ω-semigroups, Glasgow Math. J. 9 (1968), 44–66.CrossRefGoogle Scholar
15.Petrich, M., Inverse Semigroups (John Wiley and Sons, New York, 1984).Google Scholar
16.Pontryagin, L. S., Topological Groups, Second Edition (Gordon and Breach, New York, 1966).Google Scholar
17.Schein, B. M., Completions, translational hulls and ideal extensions of inverse semigroups, Czechoslovak Math. J. 23 (1973), 575–610.CrossRefGoogle Scholar