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Regular bisimple rings
Published online by Cambridge University Press: 20 January 2009
Abstract
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