Injective Modules Relative to the Dickson Torsion Theory
Septimiu Crivei
Abstract.
Let R be an associative ring with nonzero identity. An Rmodule
D is injective relative to the Dickson torsion theory (or minjective)
if any homomorphism from any maximal left ideal of R to D
extends to R. If R is commutative, I a nonzero proper
spure ideal of R and A an Rmodule such that I
\subseteq Ann_R A, we show that A is minjective as
an Rmodule if and only if A is minjective as an
R/Imodule. For certain prime ideals p of R, we also
prove some properties of the minjective hull of R/p. Thus,
if R is commutative noetherian and p a nonzero prime ideal
of R with dim R/p \geq 2, then the minjective
hull of R/p is strictly contained in Ann_{E(R/p)} p.
