Injective modules relative to the Dickson torsion theory (Q1862701)

Let \(R\) be an associative ring with 1. The author studies the injective modules relative to the Dickson torsion theory (the torsion modules are the semi-Artinian modules). For commutative rings, a change of rings result is obtained. It is shown that if \(R\) is Noetherian commutative and \(p\) is a non-zero prime ideal of \(R\) with \(\dim R/p\geq 2\), then the relative injective hull of \(R/p\) is strictly contained in \(\text{Ann}_{E(R/p)}p\), where \(E(R/p)\) denotes the injective hull of \(R/p\). Several other properties of the relative injective hull are investigated.