A subdirect decompositiono f semiprime rings and its application to maximalq uotient rings

Louis Halle Rowen

doi:10.1090/S0002-9939-1974-0349728-7

A subdirect decompositiono f semiprime rings and its application to maximalq uotient rings

Louis Halle Rowen

The University of Chicago

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English
Pages (from-to)	176-180
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	46
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1974-0349728-7
State	Published - Nov 1974
Externally published	Yes

Keywords

Essential
Injective hull
Maximal quotient ring
Semiprime
Singular ideal

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10.1090/S0002-9939-1974-0349728-7

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AB - 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.

KW - Essential

KW - Injective hull

KW - Maximal quotient ring

KW - Semiprime

KW - Singular ideal

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A subdirect decompositiono f semiprime rings and its application to maximalq uotient rings

Abstract

Keywords

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