Let R be a commutative ring. An R-module M is said to be w-flat if TorR 1 (M, N) is a GV-
torsion R-module for all R-modules N. In this paper, we study the flat and projective …

Let R be a commutative ring. An R-module M is said to be w-flat if Tor R 1 (M, N) is GV-
torsion for any R-module N. It is known that every flat module is w-flat, but the converse is not …

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 domain with its field Q of quotients. An R-module M is said to be weak w-
projective if $ Ext^ 1_R (M, N)= 0$ for all $ N {\in}{\mathcal {P}}^{\dagger} _w $, where …

Let R be a commutative ring. An R-module M is called a semi-regular w-flat module if
\Tor_1^R(R/I,M) is \GV-torsion for any finitely generated semi-regular ideal I. In this article …

Let R be a ring and let S be a multiplicative subset of R. An R‐module M is said to be au‐S‐
absolutely pure module if Ext R 1 N, M is u‐S‐torsion for any finitely presented R‐module N …

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 …

In this paper, strongly cotorsion (torsion-free) modules are studied and strongly cotorsion
(torsion-free) dimension is introduced. It is shown that every module has a special SCn …

The introduction of w-operation in the class of flat modules has been successful. Let R be a
ring. An R-module M is called aw-flat module if TOR R 1 (M, N) is GV-torsion for all R …

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 …