Let $ R $ be a ring and $\mathsf S $ be a class of strongly finitely presented (FP ${} _\infty $)
$ R $-modules closed under extensions, direct summands, and syzygies. Let $(\mathsf …

The phenomenon of periodicity, discovered by Benson and Goodearl, is linked to the
behavior of the objects of cocycles in acyclic complexes. It is known that any flat Proj …

The paper can be viewed as an addition and extension of the recent paper of Emmanouil
(2016)[5]. Among others, an alternative functor category approach to Emmanouil's results is …

Enochs' conjecture asserts that each covering class of modules (over any ring) has to be
closed under direct limits. Although various special cases of the conjecture have been …

Let R be a ring (not necessarily commutative). A left R-module is said to be cotorsion if Ext 1
R (G, M)= 0 for any flat R-module G. It is well known that each pure-injective left R-module is …

The structure of cyclically pure injective modules over a commutative ring R is investigated
and several characterizations for them are presented. In particular, we prove that a module …

We prove that all $ n $-cotilting $ R $-modules are pure-injective for any ring $ R $ and any
$ n\ge 0$. To achieve this, we prove that ${^{\perp _1} U} $ is a covering class whenever $ U …

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 …

This unique and comprehensive volume provides an up-to-date account of the literature on
the subject of determining the structure of rings over which cyclic modules or proper cyclic …

We study the behaviour of modules M that fit into a short exact sequence 0→ M→ C→ M→ 0,
where C belongs to a class of modules CC, the so-called C C-periodic modules. We find a …