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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: [email protected]
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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

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