Let C be a semidualizing R-module, where R is a commutative ring. We first introduce the
definition of C-cotorsion modules, and obtain the properties of C-cotorsion modules. As …

Let R be a commutative Noetherian ring with non-zero identity, na non-negative integer, 𝔞
an ideal of R with dim (R/𝔞)≤ n+ 1, and X an arbitrary R-module. In this paper, we prove the …

Let R be a ring and n be a positive integer. R is called left n-coherent, if every n-presented
left R-module is (n+ 1)(n+ 1)-presented. A left R-module M is called (n, 0)-injective if Ext …

Let R be a ring. An R-module N is called Gorenstein cotorsion module if Ext R 1 (F, N)= 0 for
any Gorenstein flat R-module F. We investigate some properties of Gorenstein cotorsion …

In this article, the notion of pure hereditary rings is introduced as a nontrivial generalization
of the notion of both pure semisimple rings and of hereditary rings. Some properties and …

Some Remarks on Global Dimensions for Cotorsion Pairs. Page 1 REND. SEM. MAT. UNIV.
PADOVA, Vol. 116 2006) Some Remarks on Global Dimensions for Cotorsion Pairs. EDGAR …

Let R be a ring. A right R-module M is called f-projective if Ext1 (M, N)= 0 for any f-injective
right R-module N. We prove that (F-proj, F-inj) is a complete cotorsion theory, where F-proj …

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 and let 𝒮𝒢ℱ be the class of strongly Gorenstein at right R-modules. We call a
right R-module M a weak Gorenstein cotorsion module if M is in the class 𝒮𝒢ℱ⊥. Properties …

In this paper, we introduce and study the concepts of weak n-injective and weak n-flat
modules in terms of super finitely presented modules whose projective dimension is at most …