It was shown in Dung-Smith [2] that, for a module M, every module in σ [M] is extending (CS
module) if and only if every module in σ [M] is a direct sum of indecomposable modules of …

Let T be an infinitely generated tilting module of projective dimension at most one over an
arbitrary associative ring A, and let B be the endomorphism ring of T. We prove that if T is …

A right R-module M with endomorphism ring S is called a costar module if it induces the
duality between the class of MR-torsionless right R-modules X with Hom R (X, MR) finitely …

Let A and B be two rings, M be a left B, right A bimodule and be the formal triangular matrix
ring. It is known that the category of right T-modules is equivalent to the category Ω of triples …

In this paper we shall present a property (cohopfian) which is equivalent to the cancellation
property for quasi-injective modules. Several conditions are given which imply that a quasi …

It is clear that this defintion depends on the direct decomposition of T. We have studied a
cyclic hollow module in [3]. We note that the concept dual to a cyclic hollow module is a …

Let R be a Noetherian ring and I an ideal of R. Let M be an I-cofinite and N a finitely
generated R-module. It is shown that the R-modules $ Tor_ {i}^{R}(N, M) $ are I-cofinite for …

The flat cover conjecture, saying that every module has a flat (pre) cover, has been recently
proved by Bican, El Bashir, and Enochs. We relate flat precovers (and cotorsion …

This thesis makes concrete some of the connections between the functor-categorical and
model-theoretic approaches to the study of modules over a ring. We show that the functor …

Introduction. Let R be an integral domain with quotient field Q, and let A be a module over R.
A is said to be a divisible R-module, if rA= A for every r7OER. An element xEA is said to be a …