Reduced right ideals which are strongly essential in direct summands
Let R denote an associative ring with unity and X and Y are right ideals of R. We say X is strongly essential in Y if Y is an essential extension of X and X is an essential extension of an isomorphic copy of Y. R is said to be right GFC if every faithful cyclic right R-module generates Mod-R. In this paper we show that if R satisfies any of the following conditions, then every finitely generated reduced (i.e., no nonzero nilpotent elements) right ideal is strongly essential in a direct summand of R: (i) every finitely generated reduced right ideal is essential in a direct summand of R; (ii) R is right p.p. right GFC, (iii) R is semiprime quasi-Baer right GFC. Examples of such rings are: regular rings, right CS rings, and semiprime right FPF rings.
scientific article; zbMATH DE number 4036020