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 is without nilpotent elements if and only if is a subdirect product of skew-domains. In this paper we prove that a semiprime ring with involution is a subdirect product of rings without symmetric divisors of zero if and only if is compressible for its symmetric elements.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0349737-8

Keywords:
Ring with involution,
symmetric elements,
traces,
norms,
-prime rings,
-system,
-compressible rings

Article copyright:
© Copyright 1974
American Mathematical Society