Rings whose proper (principal) right ideals are strongly compressible

Abstract

It is known that a ring [Formula: see text] is semiprime right Goldie if and only if [Formula: see text] is a strongly compressible module if and only if every right ideal of [Formula: see text] is strongly compressible, and that a ring [Formula: see text] is semiprime Goldie ring if and only if every right ideal of [Formula: see text] is weakly injective if and only if every essential right ideal of [Formula: see text] is weakly injective. In this paper, we characterize the rings whose proper (principal) right ideals are strongly compressible, and the rings whose proper (essential) right ideals are weakly injective.