On subdirect products of rings without symmetric divisors of zero

Yit, Tao Cheng

doi:10.1090/S0002-9939-1974-0349737-8

On subdirect products of rings without symmetric divisors of zero
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by Tao Cheng Yit PDF

Proc. Amer. Math. Soc. 46 (1974), 169-175 Request permission

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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