… 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 …

… The projective dimension of S/I, denoted \(\textrm{pd}_S(S/I)\), is equal to g. The … Hence,
as K is infinite, by [58, Proposition 5.6.1] we can pick a linear form h in \(\mathfrak {m}\) which is …

… 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 …

… Gorenstein ring if the total ring of quotients is a Gorenstein ring, or equivalently R p $R_{\mathfrak
{p}}$ is a Gorenstein … generically Gorenstein ring, we have the equality of G-dimension; …

… 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 …

… Finitely generated Gorenstein projective modules over a noetherian ring are introduced by
… ‘modules of G-dimension zero’ [2]. Over a commutative Gorenstein ring, these modules are …

… finite projective dimension, \(U_A\) has finite flat dimension and A is left Gorenstein regular,
… of left T-modules is equivalent to the category \({\mathfrak {C}}\) whose objects are triples \(M=…