Injective Modules Relative to the Dickson Torsion Theory 

Septimiu Crivei

Let R be an associative ring with non-zero identity. An R-module D is injective relative to the Dickson torsion theory (or m-injective) if any homomorphism from any maximal left ideal of R to D extends to R. If R is commutative, I a non-zero proper s-pure ideal of R and A an R-module such that I \subseteq Ann_R A, we show that A is m-injective as an R-module if and only if A is m-injective as an R/I-module. For certain prime ideals p of R, we also prove some properties of the m-injective hull of R/p. Thus, if R is commutative noetherian and p a non-zero prime ideal of R with dim R/p  \geq  2, then the m-injective hull of R/p is strictly contained in Ann_{E(R/p)} p.