Endo-principally quasi-Baer modules

摘要

Analogous to left p.q.-Baer property of a ring [G. F. Birkenmeier, J. Y. Kim and J. K. Park, Principally quasi-Baer rings, Comm. Algebra 29 (2001) 639-660], we say a right R-module M is endo-principally quasi-Baer (or simply, endo-p.q.-Baer) if for every m is an element of M, l(S)(Sm) = Se for some e(2) = e is an element of S = End (R) (M). It is shown that every direct summand of an endo-p.q.-Baer module inherits the property that any projective (free) module over a left p.q.-Baer ring is an endo-p.q.-Baer module. In particular, the endomorphism ring of every infinitely generated free right R-module is a left (or right) p.q.-Baer ring if and only if R is quasi-Baer. Furthermore, every principally right FI-extending right FI-K-nonsingular ring is left p.q.-Baer and every left p.q.-Baer right FI-K-cononsingular ring is principally right FI-extending.