Beck et. al. characterized the grid graphs whose perfect matching polytopes are Gorenstein and they also showed that for some parameters, perfect matching polytopes of torus graphs are Gorenstein. In this paper, we complement their result, that is, we characterize the torus graphs whose perfect matching polytopes are Gorenstein. Beck et. al. also gave a method to construct an infinite family of...

we investigate the relative cohomology and relative homology theories of $f$-gorenstein modules, consider the relations between classical and $f$-gorenstein (co)homology theories.

Motivated by their impact on homological algebra, the change of rings results have been the subject of several interesting works in Gorenstein homological algebra over Noetherian rings. In this paper, we investigate the change of rings theorems for the Gorenstein dimensions over arbitrary rings. Namely, by the use of the notion of strongly Gorenstein modules, we extend the well-known first, sec...

We describe the structure of monoid natural-valued monotone functions on an arbitrary poset. For this we provide a presentation, characterization prime elements, and description its convex hull. also study associated ring, proving that it is normal, thus Cohen-Macaulay. determine Cohen-Macaulay type, characterize Gorenstein property, Gröbner basis defining ideal. Then apply these results to qua...

We investigate the relative cohomology and relative homology theories of $F$-Gorenstein modules, consider the relations between classical and $F$-Gorenstein (co)homology theories.

Let R be a polynomial ring over field and let I ⊂ Gorenstein ideal of height three that is minimally generated by homogeneous polynomials the same degree. We compute multiplicity saturated special fiber I. The obtained formula depends only on number variables R, minimal generators I, degree syzygies Applying results from Busé et al. (Proc. Lond. Math. Soc. 121(4):743–787, 2020) we get for j-mul...

In their paper [1], H. Ananthnarayan, L. Avramov, and W.F. Moore introduced a connected sum construction for local Gorenstein rings A,B over ring T, which, in the graded Artinian case, can be viewed as an algebraic analogue of topological same name. We give two alternative descriptions this sum: first uses analogues Thom classes vector bundles Gysin homomorphisms, second is terms Macaulay dual ...

A Gorenstein A−algebra R of codimension 2 is a perfect finite A−algebra such that R ∼= ExtA(R,A) holds as R−modules, A being a Cohen-Macaulay local ring with dimA− dimA R = 2. I prove a structure theorem for these algebras improving on an old theorem of M. Grassi [Gra]. Special attention is paid to the question how the ring structure of R is encoded in its Hilbert resolution. It is shown that R...