Related papers: Rings which are almost Gorenstein

The classification of complete multipartite graphs whose edge rings are nearly Gorenstein as well as that of finite perfect graphs whose stable set rings are nearly Gorenstein is achieved.

In this note we study trace ideals of canonical modules. Characterizations of the trace ideals in terms of annihilators of certain Ext modules are given. We apply our results to study many classes of rings close to being Gorenstein that…

In this paper several quasi-Gorenstein counterparts to some known properties of Gorenstein rings are given. We, furthermore, give an explicit description of the attach prime ideals of certain local cohomology modules.

We provide a characterization of one-dimensional almost Gorenstein rings in terms of the trace ideal. As an application, we investigate the almost Gorenstein property of certain $\mathbb{Z}_2$-graded rings.

We discuss the relationship between the trace ideal of the canonical module and pseudo-Gorensteinness. In particular, under certain mild assumptions, we show that every pseudo-Gorenstein nearly Gorenstein graded domain is Gorenstein. As an…

One of the main results of this paper is the characterization of the rings over which all modules are strongly Gorenstein projective. We show that these kinds of rings are very particular cases of the well-known quasi-Frobenius rings. We…

Hochster's Monomial Conjecture and Canonical Element Conjecture date back some thirty resp. twenty years. They concern all noetherian commutative local rings, and were proved by their originator right away in equal characteristic. Thanks to…

This paper investigates the relation between the almost Gorenstein properties for graded rings and for local rings. Once $R$ is an almost Gorenstein graded ring, the localization $R_M$ of $R$ at the graded maximal ideal $M$ is almost…

In this paper, we introduce and study the rings of Gorenstein homological dimensions small or equal than 1, which we call Gorenstein (semi)hereditary rings, specially particular cases of these rings, which we call strongly Gorenstein…

We characterize Gorenstein modules over those local rings that admit a finite contracting endomorphism.

We characterize all Gorenstein rings generated by strongly stable sets of monomials of degree two. We compute their Hilbert series in several cases, which also provides an answer to a question by Migliore and Nagel.

We define, via Gorenstein homomorphisms, a class of local rings over which there exist non-trivial totally reflexive modules. We also provide a general construction of such rings, which indicates their abundance.

We provide a characterization of the almost Gorenstein property of determinantal rings of a symmetric matrix of indeterminates over an infinite field. We give an explicit formula for ranks of the last two modules in the resolution of…

We extend the notion of type sequence to rings that are not necessarily residually rational. Using this invariant we characterize different types of rings as almost Gorenstein rings and rings of maximal length.

The notion of almost Gorenstein ring given by Barucci and Fr{\"o}berg \cite{BF} in the case where the local rings are analytically unramified is generalized, so that it works well also in the case where the rings are analytically ramified.…

We consider the homotopy category of complexes of projective modules over a Noetherian ring. Truncation at degree zero induces a fully faithful triangle functor from the totally acyclic complexes to the stable derived category. We show that…

The purpose of this paper is, as part of the stratification of Cohen-Macaulay rings, to investigate the question of when the fiber products are almost Gorenstein rings. We show that the fiber product $R \times_T S$ of Cohen-Macaulay local…

In this paper, we prove that if Cohen-Macaulay local/graded rings $R_1$, $R_2$ and $R$ satisfy certain conditions regarding multiplicity and Cohen-Macaulay type, then almost Gorenstein property of $R$ implies Gorenstein properties for all…

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 of Gorenstein (weak) global dimensions at most 1, which we call…

In this paper, we study nearly Gorensteinness of Ehrhart rings arising from lattice polytopes. We give necessary conditions and sufficient conditions on lattice polytopes for their Ehrhart rings to be nearly Gorenstein. Using this, we give…