Let $ R $ be a commutative noetherian ring admitting a dualizing complex and let $\mathfrak
p $ be a prime ideal of $ R $. In this paper we investigate when $ G (R/\frak p) $ is an $ R …

Over a commutative Noetherian ring R, the Bass invariants μi (p, M) were defined for any
module M and any prime p∈ Spec R by H. Bass (Math. Z. 82, 1963, 8-28). In the first part of …

One of the open problems in Gorenstein homological algebra is: when is the class of
Gorenstein injective modules closed under arbitrary direct limits? It is known that if the class …

Let $ R $ be a commutative Noetherian ring, and let $ M $ be an $ R $-module. In earlier
papers by Bass (1963) and Roberts (1980) the Bass numbers $\mu _i (p, M) $ were defined …

Let R be a Gorenstein local ring with maximal ideal m satisfying m^3=0≠m^2. Set k=R/m
and e=rank_k(m/m^2). If e>2 and M, N are finitely generated R-modules, we show that the …

In this paper we assume that $ R $ is a Gorenstein Noetherian ring. We show that if
$(R,\mathfrak {m}) $ is also a local ring with Krull dimension $ d $ that is less than or equal to …

We prove that the class of Gorenstein injective modules is covering if and only if it is closed
under direct limits. This adds to the list of examples that support Enochs conjecture: Every …

R will denote an n-Gorenstein ring, that is, R is left and right noetherian with injective
dimension at most n on either side. R module will mean a left R-module and all modules will …

Let $(R,\mathfrak {m}) $ be a Gorenstein complete local ring. Auslander's higher delta
invariants are denoted by $\delta _R^ n (M) $ for each module $ M $ and for each integer $ n …

In this note, it is proven that if R is a right noetherian ring with id R o R<∞ and E xt R i≥ 1
(M, F)= 0 for any left R-module F with finite flat dimension, then M is Gorenstein projective; if …