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 …

On superstability in the class of flat modules and perfect rings Page 1 PROCEEDINGS OF
THE AMERICAN MATHEMATICAL SOCIETY Volume 149, Number 6, June 2021, Pages …

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 …

The pure-injective $ R $-modules are defined easily enough: as those modules which are
injective over all pure embeddings, where an embedding $ A\rightarrow B $ is said to be …

We prove that if u: K → M u: K→ M is a left minimal extension, then there exists an
isomorphism between two subrings, End _R^ M (K) End RM (K) and End _R^ K (M) End RK …

Let λ be an infinite regular cardinal. It is proved, under the assumption of the Generalized
Continuum Hypothesis, that any λ-accessible and λ-accessibly embedded subcategory 𝒦 of …

Sums of units in self-injective rings Page 1 Journal of Algebra and Its Applications Vol. 13,
No. 6 (2014) 1450020 (7 pages) c World Scientific Publishing Company DOI: 10.1142/S0219498814500200 …

We prove that each Σ-cotorsion module over an associative ring with enough idempotents is
contained in a definable class of cotorsion modules. This is closely related to the study of Σ …

Let (X, 𝒪 X) be a scheme and 𝔐 𝔬 𝔡 X be the category of all sheaves of 𝒪 X-modules.
Enochs' conjecture states that any covering class in 𝔐 𝔬 𝔡 X is closed under directed …