Baer-like decompositions of modules

on direct sums of baer modules

the notion of baer modules was defined recently

Extensions of Baer and quasi-Baer modules

On quasi-baer modules

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

extensions of baer and quasi-baer modules

Decompositions of Reflexive Modules

In a recent paper [11] we answered to the negative a question raised in the book by Eklof and Mekler [8, p. 455, Problem 12] under the set theoretical hypothesis of ♦א1 which holds in many models of set theory. The Problem 12 in [8] reads as follows: If A is a dual (abelian) group of infinite rank, is A ∼= A⊕Z? The set theoretic hypothesis we made is the axiom ♦א1 which holds in particular in G...