APPLICATIONS OF KAPLANSKY-COHEN’S THEOREM

Tran Van Dong; Nguyen Trong Bac; Nguyen Van Sanh

Tran Van Dong
Nguyen Trong Bac
Nguyen Van Sanh

Keywords: Duo modules, duo rings, Goldie modules, Goldie rings, Kaplansky-Cohen’s theorem, fully bounded modules, fully bounded rings

Abstract

In this note, we prove that for a ﬁnitely generated, quasi-projective duo right R-module M which is a self-generator, if every prime submodule of M is M-cyclic, then every submodule of M is M-cyclic.