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Completely semisimple ring semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

John Hannah ,
J. S. Richardson  and
John Zeleznikow
John Hannah
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Australia, 3052
J. S. Richardson
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Australia3052
John Zeleznikow
Affiliation:
Department of Mathematical Sciences, Northern Illinois University at De Kalb, Illinois 60115, USA
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Abstract

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Let R be a ring in which the multiplicative semigroup is completely semisimple. If R has the maximum (respectively, minimum) condition on principal multiplicative ideals. then R is semiprime artinian (respectively, a direct sum of dense rings of finite-rank linear transformations of vector spaces over division rings).

MSC classification

Secondary: 20M25: Semigroup rings, multiplicative semigroups of rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 2 , December 1980 , pp. 150 - 156
Copyright
Copyright © Australian Mathematical Society 1980

References

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