JP Journal of Algebra, Number Theory and Applications
Volume 12, Issue 2, Pages 265 - 268
(December 2008)
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RINGS WHOSE SIMPLE SINGULAR MODULES ARE FGP-INJECTIVE (II)
Farahat S. Aly (Saudi Arabia)
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of
R is a von Neumann regular ring. As a
corollary of this result we get if R
is a ring whose simple singular right R-modules
are GP-injective, then the center
of R is a von
Neumann regular ring which is a generalization of the Nam’s Proposition 3 in
[3] which states “if R is a
semiprime ring whose simple singular right R-modules
are FGP-injective, then the center
of R is a von
Neumann regular ring”. It is also shown that if R
satisfies
for
any
and
every simple singular right R-modules
are FGP-injective, then R is a reduced
weakly regular ring.