… We prove a result about the covering properties of the class of relative Gorenstein injective
… Specifically, we prove that if for every GC-injective module G, the character module G+ is GC…

… The class ℱ is said to be (pre)covering if every module has an ℱ-(pre)cover. … between
these relative Gorenstein dimensions and the 𝒫 C -projective and ℐ C -injective dimensions. …

… relative to Ext. The first is a very general and elegant way to prove the existence of covers
with … In this way we establish the existence of pure injective envelopes of complexes and we …

… injective modules is both enveloping and covering over a two sided noetherian ring such that
the character modules of Gorenstein injective … of the Gorenstein injective covers we will use …

… as a “relative” version of sheaf cohomology. Due to the result that injectivity of sheaves of …
Externally, this yields an open covering of X such that we have, for each member U of that …

… n -injective and FP n -flat complexes. We first prove the existence of special FP n -injective
preenvelopes and FP n -flat covers, which allow to consider FP n -injective coresolutions and …

… injective modules is both covering and enveloping over any commutative noetherian ring R
such that the character modules of Gorenstein injective … RG is Gorenstein injective. Another …

… flat injective) modules (see [7, 8, 9]). In particular, Guo [9] defined the relative injective envelopes
(resp., projective covers… module over extension of Artin algebras has a relative injective …

… -injective modules and of FPn-flat modules are both covering and preenveloping over any
ring R. This includes the case of FP∞-injective … is closed under extensions, then it is covering. …

… cover and its facial submanifolds. In particular, we can determine when a facial submanifold
of a small cover is |$\pi _1$|-injective … _1$|-injectivity of a facial submanifold in a small cover: …