A subdirect decomposition of semiprime rings and its application to maximal quotient rings-Reference-Cited by-同舟云学术

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

Published:1974 Issue:2 Volume:46 Page:176-180
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Rowen Louis Halle

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-046-02/S0002-9939-1974-0349728-7/S0002-9939-1974-0349728-7.pdf

Reference3 articles.

1. Lecture Notes in Mathematics, No. 49;Faith, Carl,1967

2. Unique subdirect sums of prime rings;Levy, Lawrence;Trans. Amer. Math. Soc.,1963

3. Maximal quotients of semiprime PI-algebras;Rowen, Louis Halle;Trans. Amer. Math. Soc.,1974

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