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A property of the complex semigroup algebra of a free monoid

Part of: Rings and algebras arising under various constructions Semigroups

Published online by Cambridge University Press:  09 April 2009

M. J. Crabb ,
C. M. McGregor  and
W. D. Munn
M. J. Crabb
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK, e-mail: mjc@maths.gla.ac.uk, cmm@maths.gla.ac.uk, wdm@maths.gla.ac.uk
C. M. McGregor
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK, e-mail: mjc@maths.gla.ac.uk, cmm@maths.gla.ac.uk, wdm@maths.gla.ac.uk
W. D. Munn
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK, e-mail: mjc@maths.gla.ac.uk, cmm@maths.gla.ac.uk, wdm@maths.gla.ac.uk
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Abstract

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It is shown that the complex semigroup algebra of a free monoid of rank at least two is *-primitive, where * denotes the involution on the algebra induced by word-reversal on the monoid.

MSC classification

Secondary: 16S10: Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 16S36: Ordinary and skew polynomial rings and semigroup rings 20M25: Semigroup rings, multiplicative semigroups of rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 1 , August 2006 , pp. 97 - 104
Copyright
Copyright © Australian Mathematical Society 2006

References

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