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	Volume 12, Issue 2 Pg 129 - 268 (December 2008)
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JP Journal of Algebra, Number Theory and Applications

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.

JP Journal of Algebra, Number Theory and Applications
Volume 12, Issue 2, Pages 265 - 268 (December 2008)

RINGS WHOSE SIMPLE SINGULAR MODULES ARE FGP-INJECTIVE (II)
Farahat S. Aly (Saudi Arabia)

Abstract:
Characterizations of rings whose simple right R-modules are FGP-injective are investigated. It is proved that if R is a ring whose simple singular right R-modules are FGP-injective, then the center

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.

Keywords and phrases: von Neumann regular, FGP-injective, weakly regular.

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