… also makes it possible to characterize rings of weak global dimension at most 1, and
using … X and Y with \(Y\notin {\underline{{{\mathfrak {P}}}{{\mathfrak {r}}}}}_{R\mathrm{{-}Mod}}^{-1}(X…

… Then we prove that the length of a faithful module over an Artinian Gorenstein … x\in X^\prime\setminus
\mathfrak o\) in a sufficiently small punctured neighborhood of the base point of \(X…

… We illustrate the tools on various classes of Gorenstein or relative Gorenstein Grothendieck
… In fact, it shows that an object |$T \in{\textsf{A}}$| of finite projective dimension is tilting in our …

… a homomorphic image of a Gorenstein local ring. Assume R is a normal ring of dimension at
most three … Let X be an S-module, and take \(\mathfrak {p}\in {\text {Supp}}_RX\). We find \(\…

… We show that finitely generated Cox rings are Gorenstein. … with an action of a torus of lower
dimension, see [26]. It was … If \(\mathfrak {R}(X)\) is the factorial master Cox ring of X, then …

… family of finite-dimensional algebras which affords rich … category of the category of Gorenstein
projective Λ ı $\Lambda ^\… by the positive roots for g $\mathfrak {g}$ , and they are used in […

… is a Henselian Cohen-Macaulay local ring of dimension d with a canonical module ωA. Later
we will restrict to the case when A is a Henselian Gorenstein local ring. We first discuss the …

… Δ, the size of a face F is defined to be |F|, and its dimension is … Gorenstein) if and only if
both of them are Cohen–Macaulay (… \(\mathfrak {p}\in \text {supp}_{R}(M)\) such that \(\dim R/\…

… Let I be a Gorenstein monomial ideal. Let p be the projective dimension of S/I and \({{\mathbb
{F}}}\) its graded minimal free resolution. Then \(F_p=S(-{{\mathbf {a}}})\) and \({{\mathbb {F}}…

… Precisely, using PMs of a consistent dimer model, we define the PM polygon Δ (see Subsection
2.2) and the 3-dimensional Gorenstein toric ring R, which will be called toric singularity, …