We introduce the notion of strongly ω -Gorenstein modules, where ω is a faithfully balanced self-orthogonal module. This gives a common generalization of both Gorenstein projective (injective) modules and ω-Gorenstein modules. We investigate some characterizations of strongly ω -Gorenstein modules. Consequently, some properties under change of rings are obtained. Keywords—faithfully balanced se...

In this paper we describe the facets cone associated to transversal polymatroid presented by A = {{1, 2}, {2, 3}, . . . , {n−1, n}, {n, 1}}. Using the Danilov-Stanley theorem to characterize the canonicale module, we deduce that the base ring associated to this polymatroid is Gorenstein ring. Also, starting from this polymatroid we describe the transversal polymatroids with Gorenstein base ring...

An artin algebra A is said to be CM-finite if there are only finitely many, up to isomorphisms, indecomposable finitely-generated Gorenstein-projective A-modules. We prove that for a Gorenstein artin algebra, it is CM-finite if and only if every its Gorenstein-projective module is a direct sum of finitely-generated Gorenstein-projective modules.

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.

‎Let $C$ be a semidualizing module‎. ‎We first investigate the properties of‎ ‎finitely generated $G_C$-projective modules‎. ‎Then‎, ‎relative to $C$‎, ‎we introduce and study the rings over which‎ ‎every submodule of a projective (flat) module is $G_C$-projective (flat)‎, ‎which we call $C$-Gorenstein (semi)hereditary rings‎. ‎It is proved that every $C$-Gorenstein hereditary ring is both cohe...

It was proved by Beligiannis and Krause that over certain Artin algebras, there are Gorenstein flat modules which are not direct limits of finitely generated Gorenstein projective modules. That is, these algebras have no Gorenstein analogue of the Govorov-Lazard Theorem. We show that, in fact, there is a large class of rings without such an analogue. Namely, let R be a commutative local noether...

Motivated by some properties satisfied Gorenstein projective and injective modules over an Iwanaga-Gorenstein ring, we present the concept of left right n-cotorsion pairs in abelian category C. Two classes A B objects C form a pair (A,B) if orthogonality relation ExtCi(A,B)=0 is for indexes 1≤i≤n, every object has resolution whose syzygies have B-resolution dimension at most n−1. This its dual ...

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