In basic homological algebra, the flat and injective dimensions of modules play an important
and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions …

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 (A, B) be a cotorsion pair in R-Mod. We define and study notions of A dimension and B
dimension of unbounded complexes, which is given by means of dg-projective resolution …

In this article, we introduce the concept of IFP-flat (resp., IFP-injective) modules as nontrivial
generalization of flat (resp., injective) modules. We investigate the properties of these …

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 …

Several authors have been interested in cotorsion theories. Among these theories we figure
the pairs $(\mathcal P_n,\mathcal P_n^{\perp}) $, where $\mathcal P_n $ designates the set …

In this paper, we show that the injective dimension of all projective modules over a
countable ring is bounded by the self-injective dimension of the ring. We also examine the …

In this paper, we study the class of complexes of FP-injective left R-modules. It is shown that
the pair is a complete cotorsion pair. If R is a left coherent ring, it is proved that every …

In this paper, we investigate Ding projective dimensions and Ding injective dimensions of
modules and rings. Let R be a ring with rDPD (R)= n<℞, and let W 1={M| fd (M)<℞}. We …