We consider a ring R such that the class of Gorenstein injective modules is closed under
direct limits. We prove that the class of dg-Gorenstein injective complexes is covering in Ch …

Let A/S be a ring extension with S commutative. We prove that ω⊗ S AA is a generalized
tilting module if ωS is a generalized tilting module. In this case, we obtain that⊥ ω-resol …

Abstract Let R⊂ S be a Frobenius extension of rings and M a left S-module and let 𝓧 be a
class of left R-modules and 𝒚 a class of left S-modules. Under some conditions it is proven …

In this paper, we study the pair (GP(R),GP(R)^⊥) where GP(R) is the class of all Gorenstein
projective modules. We prove that it is a complete hereditary cotorsion theory, provided …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact …

The notion of an $\mathcal {L} $ complex (for a given class of $ R $-modules $\mathcal {L} $)
was introduced by Gillespie: a complex $ C $ is called $\mathcal {L} $ complex if $ C $ is …

A left and right Noetherian ringRis called Gorenstein if bothRRandRRhave finite injective
dimensions. These rings were studied by Bass for the commutative case and Iwanaga for …

Let R be a commutative Noetherian ring of Krull dimension d, and let a be an ideal of R. In
this paper, we will study the strong cotorsioness and the Gorenstein injectivity of the section …

We prove that the class of Gorenstein projective modules is special precovering over any left
GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every …

The purpose of this paper is to give, via totally different techniques, an alternate proof to the
main theorem of [18] in the category of modules over an arbitrary ring R. In effect, we prove …