We prove that for a left and right Noetherian ring $ R $, $ _RR $ satisfies the Auslander
condition if and only if so does every flat left $ R $-module, if and only if the injective …

We characterize left Noetherian rings in terms of the duality property of injective
preenvelopes and flat precovers. For a left and right Noetherian ring R, we prove that the flat …

If R is left noetherian and M is a left R-module, then we can construct a complex called an
injective resolvent of M using injective precovers. Likewise, if R is left coherent and M is a …

It is now well known that the conditions used by Auslander to define the Gorenstein
projective modules on Noetherian rings are independent. Recently, Ringel and Zhang …

In this paper, we introduce and study (weak) pure-injective Gorenstein projective modules.
Let R be an Artin algebra. We prove that the category of weak pure-injective Gorenstein …

Let R be a commutative Noetherian ring and A an Artinian R-module. We prove that if A has
finite Gorenstein injective dimension, then A possesses a Gorenstein injective envelope …

Let A be an artin algebra. An A-module M is semi-Gorenstein-projective provided that Ext i
(M, A)= 0 for all i≥ 1. If M is Gorenstein-projective, then both M and its A-dual M∗ are semi …

In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an
R-module M, we show that M is Gorenstein injective if and only if Hom R (Ȓ, M) belongs to …

Let A be an artin algebra. An A-module M will be said to be semi-Gorenstein-projective
provided that Ext i (M, A)= 0 for all i≥ 1. All Gorenstein-projective modules are semi …

Let A be a noetherian Auslander regular ring and δ the canonical dimension function on A-
modules, which is defined as δ (M)= d− j (M) where d is the global dimension of A and j (M) …