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

 

A subdirect decomposition of semiprime rings and its application to maximal quotient rings


Author: Louis Halle Rowen
Journal: Proc. Amer. Math. Soc. 46 (1974), 176-180
MSC: Primary 16A12
MathSciNet review: 0349728
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Abstract: Levy [2] has examined semiprime rings which are irredundant subdirect products of prime rings. In this note we look at the role of inessential prime ideals and see how every semiprime ring is a subdirect product of (i) a semiprime ring which is an irredundant subdirect product of prime rings, and (ii) a semiprime (nonprime) ring, all of whose prime ideals are essential. This leads to a direct sum decomposition of maximal left quotient rings of semiprime rings with left singular ideal zero.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0349728-7
PII: S 0002-9939(1974)0349728-7
Keywords: Essential, injective hull, maximal quotient ring, semiprime, singular ideal
Article copyright: © Copyright 1974 American Mathematical Society