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.
@article{urn:eudml:doc:41269,
title = {New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.},
journal = {Publicacions Matem\`atiques},
volume = {40},
year = {1996},
pages = {383-385},
mrnumber = {MR1425625},
zbl = {0869.16005},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41269}
}
Faith, Carl. New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.. Publicacions Matemàtiques, Tome 40 (1996) pp. 383-385. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41269/