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

Publicacions Matemàtiques (1996)

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

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topFaith, 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 -