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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
DOI: https://doi.org/10.1090/S0002-9939-1974-0349737-8
MathSciNet review: 0349737
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Abstract: A theorem of V. A. AndrunakieviÄŤ 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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Keywords: Ring with involution, symmetric elements, traces, norms, <IMG WIDTH="15" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$^ \ast$">-prime rings, <IMG WIDTH="23" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$m$">-system, <IMG WIDTH="15" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$^ \ast$">-compressible rings
Article copyright: © Copyright 1974 American Mathematical Society