Let R be a commutative ring and C a semidualizing R-module. For a non-negative integer n,
we study a natural generalization of copure injective (flat) modules by introducing the …

The flat dimensions of injective modules Page 1 manuscripta math. 78, 165- 177 (1993)
manuscripta mathematica Spfinger-Verlag 1~3 THE FLAT DIMENSIONS OF INJECTIVE …

In this paper, we generalize, with respect to the w-operation, the notions of FI-injective and FI-
flat modules introduced by L. Mao and N. Ding. Let R be a ring. An R-module M is called w …

It is well known that the right global dimension of a ring R is usually computed by the right
derived functors of Hom and the left projective resolutions of right R-modules. In this paper …

The global dimension gldim (R) of a Noetherian ring R, while a useful invariant when finite,
is often infinite. Several homological dimensions have been introduced to handle rings of …

Let $ R $ be a domain. It is proved that $ R $ is coherent when $ IFD (R)\lst1 $, and $ R $ is
Noetherian when $ IPD (R)\lst1 $. Consequently, $ R $ is a $ G $-Pr $\rm\ddot {u} $ fer …

In Section 1 of this paper, we investigate the finitely presented dimension of an essential
extension for a module, and obtain results concerning an essential extension of a torsion …

For a ring R, we prove that all left R-modules have weak injective covers and weak injective
preenvelopes. Then we characterize the right weak injective dimension of modules in terms …

We study torsionfree and divisible dimensions in terms of right derived functors of-⊗-. We
also investigate the cotorsion pair cogenerated by the class of cyclic torsionfree right R …

Let R be a ring. A left R-module M (respectively right R-module N) is called FI-injective
(respectively FI-flat) if Ext1 (G, M)= 0 (respectively Tor1 (N, G)= 0) for any FP-injective left R …