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 …

The central aim of this book is to understand modules and the categories they form through
associated structures and dimensions, which reflect the complexity of these, and similar …

Most of the model theory of modules works, with only minor modifications, in much more
general additive contexts (such as functor categories, categories of comodules, categories of …

We use the type theory for rings of operators due to Kaplansky to describe the structure of
modules that are invariant under automorphisms of their injective envelopes. Also, we …

We introduce the new concept of cartesian module over a pseudofunctor R from a small
category to the category of small preadditive categories. Already the case when R is a (strict) …

Let TR be a 1-tilting module with tilting torsion pair (Gen T, F) in Mod-R. The following
conditions are proved to be equivalent:(1) T is pure projective;(2) Gen T is a definable …

For a module-finite algebra over a commutative noetherian ring, we give a complete
description of flat cotorsion modules in terms of prime ideals of the algebra, as a …

We study the class of modules which are invariant under idempotents of their envelopes. We
say that a module M is X-idempotent-invariant if there exists an X-envelope u: M→ X such …

Let R be an associative ring with identity. It is shown that every Σ-cotorsion left R-module
satisfies the descending chain condition on divisibility formulae. If R is countable, the …

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 …