An additive functor from the category of flat right R‐modules to the category of abelian
groups is continuous if it is isomorphic to a functor of the form−⊗ RM, where M is a left R …

If R is an associative ring with identity, a theory of minimal flat resolutions is developed in the
category ((R-mod) op, Ab) of contravariant functors G:(R-mod) op→ Ab from the category R …

Let R be a ring, na fixed nonnegative integer and In (Fn) the class of all left (right) R-modules
of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n …

The aim of this paper is to describe the classes of strongly flat and weakly cotorsion modules
with respect to a multiplicative subset or a finite collection of multiplicative subsets in a …

Foxby duality has proven to be an important tool in studying the category of modules over a
local Cohen-Macaulay ring admitting a dualizing module. Recently the notion of a semi …

Let R be a ring, M a right R-module, and na fixed non-negative integer. M is called n-
cotorsion if for any flat right R-module N. M is said to be n-flat if for any n-cotorsion right R …

It is not known whether modules over an arbitrary ring have flat covers, however for certain
modules over commutative noetherian rings they can be shown to exist. These covers, in …

Let R be an associative ring with identity. A right R-module M is called cotorsion if Ext"(F,
M)= 0 for every flat right R-module F. These modules were introduced by Harrison [21] in the …

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 …

In [8] Sake introduced the notion of a cotorsion pair (A, B) in the category of abelian groups.
But his definitions and basic results carry over to more general abelian categories and have …