If $ R $ is a ring with 1, we call a unital left $ R $-module $ M $ co-Hopfian (Hopfian) in the
category of left $ R $-modules if any monic (epic) endomorphism of $ M $ is an …

In this short paper, the homological functors are used to show that a simple module is flat if
and only if it is injective. It is used to give a characterization of Von Neumann regular ring …

THEOREM L (a) A right R-module A is finitely generated if and only if for any collection {Ca}
of left R-modules, the natural map A (x) ΠCa-+ Π (A® Ca) is surjective.(b) A right R-module A …

Two pairs of functors play an outstanding role in the representation theory of finite-
dimensional tensor algebras: The Coxeter functors C^{+} and C^{-} and the functors DTr and …

We show that if a class of modules is closed under pure quotients, then it is precovering if
and only if it is covering, and this happens if and only if it is closed under direct sums. This is …

In [1], PE Bland has studied the strongly M-projective module and the strongly M-projective
cover. As their generalnotions, we define the strongly $\eta $-projective module and the …

In this paper we study the depth of tensor products of homologically finite complexes over
commutative Noetherian local rings. As an application of our main result, we determine new …

It is shown that the category of enriched functors [C, V] is Grothendieck whenever V is a
closed symmetric monoidal Grothendieck category and C is a category enriched over V …

Tensor products of ideal systems and their modules Page 1 Pacific Journal of Mathematics
TENSOR PRODUCTS OF IDEAL SYSTEMS AND THEIR MODULES KARL EGIL AUBERT AND …

Let R be a commutative ring with identity and τ be a hereditary torsion theory on R-Mod. In
this article, we introduce and study the concept of τ-comultiplication module. We present …