This paper aims at studying the homotopy category of cotorsion flat left modules K (CotF-R)
K (CotF-R) over a ring R. We prove that if R is right coherent, then the homotopy category K …

A general principle suggests that" anything flat is a directed colimit of countably presentable
flats". In this paper, we consider resolutions and coresolutions of modules over a countably …

A module UR is couniform if it has dual Goldie dimension 1, that is, it is non-zero and the
sum of any two proper submodules of UR is a proper submodule of UR. A module MR is …

In this paper quasi-codivisible covers are defined and investigated relative to a torsion
theory (T, F) on Mod R. It is shown that if (T, F) is cohereditary, then a right R-module M has a …

We introduce a general version of the singular compactness theorem which makes it
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …

Let $ R $ and $ S $ be rings with unit. Suppose $ P $ is a free $ R $-module on $\beta $
generators, where $\beta $ is an infinite cardinal number not smaller than the cardinality of …

A cotorsion theory is defined as a pair of classes Ext-orthogonal to each other. We give a
hereditary condition (HC) which is satisfied by the (flat, cotorsion) cotorsion theory and give …

The modules of the title are introduced as a proper generalization of quasi co-Hopfian
modules, and they are characterized in several ways. The ring R is right nonsingular if and …