… 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 …

… 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 …

… (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, …

… studied Gorenstein homological dimensions for triangulated categories with ξ-Gorenstein …
The ξ-projective dimension ξ-pdA of an object A is defined inductively. When A “ 0, put ξ-pdA …

… 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. …

… An R-module M has rank if \(M_{\mathfrak {p}}\) is free of constant rank r for all associated
primes \(\mathfrak {p}\) of R; in this case, we write rank R (M) = r. We say M is Cohen-Macaulay …

… dimensional torus T). As an application we conclude that any d-dimensional complex
smooth projective variety X equipped with an integral Kähler form has a proper (d − 1)-dimensional …

… there is a homogeneous valuation |${\mathfrak {v}}: R \… $|-dimensional complex smooth
projective variety |$X$| equipped with an integral Kähler form has a proper |$(d-1)$|-dimensional …