A class of small injective modules

الملخص EN

Let R be a ring.

In this paper, a right R-module M is defined to be AS-injective if Ext1 (R ⁄K, M )=0 , for any annihilator-small right ideal K of R .

We characterize rings over which every right module is AS-injective.

Conditions under which the class of AS-injective right R-modules (ASIr ) is closed under quotient (resp.

pure submodules, direct sums) are given.

Finally, we study the definability of the class ASIr.