Matlis injective modules. (Q2856987)

This paper introduces the notion of Matlis injective modules. A right \(R\)-module \(M\) is called Matlis injective if \(\text{Ext}^1(E(R),M)=0\), where \(E(R)\) denotes the injective envelope of \(R\). It is shown among other things that every right \(R\)-module has a Matlis injective preenvelope and every right \(R\)-module has a Matlis injective envelope when \(R\) is a right Noetherian ring.