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 …

Chapter 19 The Cotorsion Dimension of Modules and Rings Lixin Mao Department of Basic
Courses, Nanjing Institute of Technology, Nanjing 210013, Peoples Republic of China …

Let R be a ring. We define a dimension, called P-cotorsion dimension, for modules and
rings. The aim of this article is to investigate P-cotorsion dimensions of modules and rings …

We extend the cotorsion dimension of R-modules to unbounded R-complexes by applying
the flat model structure on Ch (R) proposed by J. Gillespie. This is not natural because there …

Let (𝒳, 𝒴) be a complete and hereditary cotorsion pair in a bicomplete abelian category 𝒜.
We introduce a Gorenstein category 𝒢 (𝒳) and 𝒢 (𝒳)-resolution dimension of complexes …

We construct Abelian model structures on the category of chain complexes over a ring $ R $,
from the notion homological dimensions of modules. Given an integer $ n> 0$, we prove that …

Let R be a left Noetherian ring, S a right Noetherian ring and RU a generalized tilting
module with S= End (RU). We give some equivalent conditions that the injective dimension …

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 …

We construct Abelian model structures on the category of chain complexes over a ring 𝑅,
from the notion of homological dimensions of modules. Given an integer, 𝑛> 0, we prove that …

Consider a class C of projective R-modules, where R is a commutative ring with identity,
which satisfies the conditions of (2), namely that C is closed under the operations of direct …