New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.

Carl Faith

Publicacions Matemàtiques (1996)

  • Volume: 40, Issue: 2, page 383-385
  • ISSN: 0214-1493

Abstract

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A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when R itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.

How to cite

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Faith, Carl. "New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.." Publicacions Matemàtiques 40.2 (1996): 383-385. <http://eudml.org/doc/41269>.

@article{Faith1996,
abstract = {A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when R itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.},
author = {Faith, Carl},
journal = {Publicacions Matemàtiques},
keywords = {Teoría de anillos; Ideal maximal; Anillos de Von Neumann; von Neumann regular rings; Jacobson radical; maximal von Neumann regular ideals; semiprime rings; annihilator ideals; finite products of simple ideals},
language = {eng},
number = {2},
pages = {383-385},
title = {New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.},
url = {http://eudml.org/doc/41269},
volume = {40},
year = {1996},
}

TY - JOUR
AU - Faith, Carl
TI - New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.
JO - Publicacions Matemàtiques
PY - 1996
VL - 40
IS - 2
SP - 383
EP - 385
AB - A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when R itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.
LA - eng
KW - Teoría de anillos; Ideal maximal; Anillos de Von Neumann; von Neumann regular rings; Jacobson radical; maximal von Neumann regular ideals; semiprime rings; annihilator ideals; finite products of simple ideals
UR - http://eudml.org/doc/41269
ER -

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