We describe in homological terms the direct limit closure of a class C of modules over a ring
R. We also determine the closure of the cotorsion pair=(A, B) cogenerated by C. As an …

We apply the theory of cotorsion pairs to study closure properties of classes of modules with
finite projective dimension with respect to direct limit operations and to filtrations. We also …

The remarkable success of the homological study of modules with finite free resolutions has
over a number of years largely determined the focus of attention in commutative algebra. It is …

Let R be a ring and T an (infinitely generated) tilting module. Then T is of countable type; that
is, there is a set, 𝒞, of modules possessing a projective resolution consisting of countably …

Given a ring $ R $, two classes $\mathcal A $ and $\mathcal B $ of $ R $-modules are said
to form a cotorsion pair $(\mathcal A,\mathcal B) $ in $\operatorname {Mod} R $ if $\mathcal …

We generalize Hill's lemma in order to obtain a large family of C-filtered submodules from a
single C-filtration of a module. We use this to prove the following generalization of …

Let J be a directed set and let {Λj, φij} be a direct system of rings indexed by J and with limit
Λ. Let {Aj, φij} be a direct system of groups indexed by J. Assume that each Aj is a left Λj …

We show that a direct limit of projective contramodules (over a right linear topological ring) is
projective if it has a projective cover. A similar result is obtained for-strictly flat contramodules …

However, some aspects of the classical theory can be extended to infinitely generated
modules over arbitrary rings. In this paper, we will consider such an aspect: the relation of …

Core of projective dimension one modules Page 1 manuscripta math. 111, 427–433 (2003) ©
Springer-Verlag 2003 Alberto Corso · Claudia Polini · Bernd Ulrich Core of projective dimension …