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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On subdirect products of rings without symmetric divisors of zero


Author: Tao Cheng Yit
Journal: Proc. Amer. Math. Soc. 46 (1974), 169-175
MSC: Primary 16A28
MathSciNet review: 0349737
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Abstract: A theorem of V. A. Andrunakievič and Ju. M. Rjabuhin asserts that a ring $ R$ is without nilpotent elements if and only if $ R$ is a subdirect product of skew-domains. In this paper we prove that a semiprime ring $ R$ with involution is a subdirect product of rings without symmetric divisors of zero if and only if $ R$ is compressible for its symmetric elements.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0349737-8
PII: S 0002-9939(1974)0349737-8
Keywords: Ring with involution, symmetric elements, traces, norms, $ ^ \ast $-prime rings, $ m$-system, $ ^ \ast $-compressible rings
Article copyright: © Copyright 1974 American Mathematical Society