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Regular bisimple rings

Published online by Cambridge University Press:  20 January 2009

John Hannah
John Hannah
Affiliation:
Mathematics DepartmentUniversity Of CanterburyChristchurch, New Zealand
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Abstract

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We characterize regular bisimple rings in terms of some perspectivity conditions on their lattices of principal right ideals. We also show that, if S is the multiplicative subsemigroup generated by all the idempotents of a regular bisimple ring R, then

(i) if R does not have an identity, then S = R and has depth 2;

(ii) if R does have an identity but is not a division ring, then S = {a∈R:a is neither left nor right invertible} ∪ {1} and has depth 3.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 1 , February 1991 , pp. 89 - 97
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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