… all projective R-modules) are denoted by … projective dimension and Gorenstein projective
dimension of M. We always assume that X is a class of R-modules which contains all projective …

… projective resolution and ξ-Gprojective resolution for any object A in C. What is more, we define
a particular ξGorenstein projective … of G-dimension zero modules, and dually they defined …

… We prove that for a Gorenstein ring, the stable category of Gorenstein-projective modules
is … has finite projective dimension. Thus we infer that K has finite projective dimension. Note …

… Recall that a ring R is called right Gorenstein regular [9] if the classes of modules with finite
projective dimension and with finite injective dimension coincide. Moreover, a duality pair is a …

… s G-dimension extends the notion of projective dimension, and its finiteness characterizes
Gorenstein … In particular, if T has finite projective dimension over Rp, we can conclude that Ext i …

… (M)\), in case M is an R-module and \(x\in \mathfrak {m}\) is a non zero-divisor on R and M. …
,}}_R(M)\) in case M is an R-module and \(x\in \mathfrak {m}\) is a non zero-divisor on R and M, …

… \(\Lambda\)-modules are also known in the literature as modules of Gorenstein dimension
zero or totally reflexive (see [1, 5, §2]). We denote by \(\Lambda\)-Gproj the category of …

… every finitely generated module has finite Gorenstein dimension are precisely the Gorenstein
rings. … ideal |$\mathfrak n=(x,y,z)$|⁠, embedding dimension 3, Loewy length 3 and length 6. …

… Gorenstein projective dimension of a ring R is equal to the global Gorenstein injective
dimension … Ren and Liu in [14] studied Gorenstein homological dimensions for triangulated …

… ring \((R,\mathfrak m)\) is Gorenstein if and only if it admits an … (\mathfrak m\)-primary ideal of
finite Gorenstein dimension. This … Gorenstein dimension, but not that of projective dimension. …