A module MR is called right principally quasi-Baer (or simply right p.q.-Baer) if the right annihilator of a principal submodule of R is generated by an idempotent. Let R be a ring. Let α be an endomorphism of R and MR be a α-compatible module and T = R[[x;α]]. It is shown that M [[x]]T is right p.q.-Baer if and only if MR is right p.q.-Baer and the right annihilator of any countably-generated ...

In this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.

In this paper, the notion of fully idempotent modules is defined and it is shown that this notion inherits most of the essential properties of the usual notion of von Neumann's regular rings. Furthermore, we introduce the dual notion of fully idempotent modules (that is, fully coidempotent modules) and investigate some properties of this class of modules.

in this paper, the notion of fully idempotent modules is defined and it is shown that this notion inherits most of the essential properties of the usual notion of von neumann's regular rings. furthermore, we introduce the dual notion of fully idempotent modules (that is, fully coidempotent modules) and investigate some properties of this class of modules.

in this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.

In two recent papers [9, 10] we answered a question raised in the book by Eklof and Mekler [7, p. 455, Problem 12] under the set theoretical hypothesis of ♦א1 which holds in many models of set theory, respectively of the special continuum hypothesis (CH). The objects are reflexive modules over countable principal ideal domains R, which are not fields. Following H. Bass [1] an R-module G is refl...

In this paper, we introduce and investigate the notion of projection invariant semisimple modules. Some structural properties aforementioned class modules are studied. We obtain indecomposable decompositions former under some module theoretical conditions. Moreover, explore when finite exchange property implies full for Finally, that endomorphism ring a is ?- Baer ring.

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

We study finiteness conditions on large tilting modules over arbitrary rings. We then turn to a hereditary artin algebra R and apply our results to the (infinite dimensional) tilting module L that generates all modules without preprojective direct summands. We show that the behaviour of L over its endomorphism ring determines the representation type of R. A similar result holds true for the (in...