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Strongly regular near-rings

Published online by Cambridge University Press:  20 January 2009

Gordon Mason
Gordon Mason
Affiliation:
University of New BrunswickFredericton, N.B., Canada
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A strongly regular ring R is one in which for all x ∈ R, there is an a ∈ R with x = x2a. Equivalently, for all x there is an a with x = ax2. Such a ring is regular, duo, biregular, and a left and right V-ring. Moreover since R is reduced, all nilpotent elements are central (vacuously) and so all idempotent elements are central.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 1 , February 1980 , pp. 27 - 35
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

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