Related papers: Pseudo-Gorenstein and level Hibi rings

In this paper, we state criteria of a Hibi ring to be level, non-Gorenstein and almost Gorenstein and to be non-level and almost Gorenstein in terms of the structure of the partially ordered set defining the Hibi ring. We also state a…

Let $L$ be a distributive lattice and $R[L]$ the associated Hibi ring. We show that if $L$ is planar, then any bounded Hibi subring of $R[L]$ has a quadratic Gr\"obner basis. We characterize all planar distributive lattices $L$ for which…

We classify path polyominoes which are level and pseudo-Gorenstein. Moreover, we compute all level and pseudo-Gorenstein simple thin polyominoes with rank less than or equal to 10. We also compute the regularity of the pseudo-Gorenstein…

Levelness and nearly Gorensteinness are well-studied properties of graded rings as a generalized notion of Gorensteinness. In this paper, we compare the strength of these properties. For any Cohen-Macaulay homogeneous affine semigroup ring…

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…

We describe the non-Gorenstein loci of normal toric varieties. In the case of Hibi rings a combinatorial description is provided in terms of the underlying partially ordered set. As a non-toric application we compute the dimensions of the…

Let $L$ be a distributive lattice and $R(L)$ the associated Hibi ring. We compute $\reg R(L)$ when $L$ is a planar lattice and give a lower bound for $\reg R(L)$ when $L$ is non-planar, in terms of the combinatorial data of $L.$ As a…

Let $K$ be a field, $D$ a finite distributive lattice and $P$ the set of all join-irreducible elements of $D$. We show that if $\{y\in P\mid y\geq x\}$ is pure for any $x\in P$, then the Hibi ring $\RRRRR_K(D)$ is level. Using this result…

In this paper we consider Hibi rings and Rees rings attached to a poset. We classify the ideal lattices of posets whose Hibi relations are indispensable and the ideal lattices of posets whose Hibi relations form a quadratic Groebner basis…

We compute the regularity of the Hibi ring of any finite distributive lattice in terms of its poset of join irreducible elements.

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…

Semi-standard graded rings are a generalized notion of standard graded rings. In this paper, we compare generalized notions of the Gorenstein property in semi-standard graded rings. We discuss the commonalities between standard graded rings…

A lattice polytope $\mathcal{P} \subset \mathbb{R}^n$ of dimension $n$ is called level* if (i) $\mathcal{P}$ is normal, (ii) $(\mathcal{P} \setminus \partial \mathcal{P}) \cap \mathbb{Z}^n \neq \emptyset$ and (iii) for each $N = 2,3,…

We recall the projective variety parametrizing a family of special lattices over Witt vectors. It is normal and Gorenstein. In this article, we prove that there exists a particular set of subvarieties in it that are also normal and…

We define the concept of a doset Hibi ring and a generalized doset Hibi ring which are subrings of a Hibi ring and are normal affine semigrouprings. We apply the theory of (generalized) doset Hibi rings to analyze the rings of absolute…

Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical…

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…

The Alexander dual of an arbitrary meet-semilattice is described explicitly. Meet-distributive meet-semilattices whose Alexander dual is level are characterized.

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…

This paper introduces and studies a particular subclasses of the class of commutative rings with finite Gorenstein global (resp., weak) dimensions.