Let R be a ring. A right R-module A is said to be C-flat if the kernel of any epimorphism B→ A
is C-pure in B, ie the induced map Hom (C, B)→ Hom (C, A) is surjective for any cyclic right …

In this article, FP-injective complexes are introduced and studied. We prove that (⊥ ℱℐ, ℱℐ)
is a hereditary cotorsion theory if and only if R is a left coherent ring, where ℱℐ denotes the …

Equivalences and Dualities between FCI and FGP Modules 1 Introduction Page 1 International
Journal of Algebra, Vol. 3, 2009, no. 19, 911 - 918 Equivalences and Dualities between FCI …

Rg be a G-graded ring. It is well known (see eg [D],[M1],[N],[NRV],[NV]) that in the study of
the connections that may be established between the categories R-gr of graded R-modules …

Let Mod-S denote the category of S-modules, where S is a small pre-additive category.
Using the notion of relative derived categories of functor categories, we generalize Rickard's …

For a nonempty topological space $ X $, the ring of all real-valued functions on $ X $ with
pointwise addition and multiplication is denoted by $ F (X) $ and contonuous members of …

It is known that if R is a ring with identity, and S and A op are the functor rings associated to
the categories Mod (R) and Mod (R op), respectively, then there is a duality between the …

For a category, we investigate the problem of when the coproduct⊕ and the product
functor∏ from I to are isomorphic for a fixed set I, or, equivalently, when the two functors …

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 …

A commutative ring $ R $ is $ F {P^ 2} F $(resp. FPF) provided that all finitely presented
(resp. finitely generated) faithful modules generate the category $\bmod-R $ of all $ R …