JP Journal of Algebra, Number Theory and Applications
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Abstract: Characterizations
of rings whose simple right R-modules
areFGP-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
areGP-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
areFGP-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.
