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Can a Semi-Prime Ring be a Finite Union of Right Annihilators?

Published online by Cambridge University Press:  20 November 2018

Charles Lanski
Charles Lanski*
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113
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Abstract

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The interesting question of the title was posed by J. Bergen and this note answers it in the negative. The main result characterizes rings which can be a finite union of proper right annihilators, and shows that any such commutative ring must have a total annihilator.

Keywords

16A3416A1216A48
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 126 - 128
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Herstein, I. N., Noncommutative Rings, The Cams Mathematical Monographs, No. 15, The Mathematical Association of America, 1968.Google Scholar
2. Neumann, B. H., Groups covered by permutable subsets, J. Lond. Math. Soc, 29 (1954), 236–248.Google Scholar