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Moore-Penrose inversion in complex contracted inverse semigroup algebras

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

W. D. Munn
W. D. Munn
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK e-mail: wdm@maths.gla.ac.uk
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Abstract

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It is shown that every element of the complex contracted semigroup algebra of an inverse semigroup S = S0 has a Moore-Penrose inverse, with respect to the natural involution, if and only if S is locally finite. In particular, every element of a complex group algebra has such an inverse if and only if the group is locally finite.

MSC classification

Secondary: 20M25: Semigroup rings, multiplicative semigroups of rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 3 , June 1999 , pp. 297 - 302
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Math. Surveys of the Amer. Math. Soc. 7 (Providence R.I., 1961 (vol. I) and 1967 (vol. II)).Google Scholar
[2]Moore, E. H., ‘On the reciprocal of the general algebraic matrix’, Bull. Amer. Math. Soc. 26 (1920), 394–395.Google Scholar
[3]Munn, W. D., ‘Matrix representations of semigroups’, Proc. Cambridge Philos. Soc. 53 (1957), 5–12.CrossRefGoogle Scholar
[4]Munn, W. D., ‘Semiprimitivity of inverse semigroup algebras’, Proc. Roy. Soc. Edinburgh. Sect. A 93 (1982), 83–98.CrossRefGoogle Scholar
[5]Okniński, J., ‘On regular semigroup rings’, Proc. Roy. Soc. Edinburgh, Sect. A 99 (1984), 145–151.CrossRefGoogle Scholar
[6]Penrose, R., ‘A generalized inverse for matrices’, Proc. Cambridge Philos. Soc. 51 (1955), 406–413.CrossRefGoogle Scholar
[7]Penrose, R., ‘On best approximate solutions of linear matrix equations’, Proc. Cambridge Philos. Soc. 52 (1956), 17–19.CrossRefGoogle Scholar
[8]Shehadah, A. A., Embedding theorems for semigroups with involution (Ph.D. Thesis, Purdue University, Indiana, 1982).Google Scholar