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 …

It is possible to associate a topological space to the category of modules over any ring. This
space, the Ziegler spectrum, is based on the indecomposable pure-injective modules …

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 $ T $ be a $1 $-tilting module whose tilting torsion pair $({\mathcal T},{\mathcal F}) $ has
the property that the heart ${\mathcal H} _t $ of the induced $ t $-structure (in the derived …

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 …

RINGS OVER WHICH FLAT COVERS OF SIMPLE MODULES ARE PROJECTIVE Page 1
Journal of Algebra and Its Applications Vol. 11, No. 3 (2012) 1250046 (7 pages) c© World …