Level rings arising from meet-distributive meet-semilattices

The monomial ideal of a finite meet-semilattice

Squarefree monomial ideals arising from finite meet-semilattices and their free resolutions are studied. For the squarefree monomial ideals corresponding to poset ideals in a distributive lattice the Alexander dual is computed.

半格同余的成对分配律

The pairwise distributive law of semilattice congruences

本文证明半格同余格相对于主同余满足分配形式，建立了任意同余族（含无限集）的“成对分配律”。

分配格的join-meet二项代数

Join-meet binomial algebras of distributive lattices

研究有限分配格生成的join-meet二项代数定义理想，探讨其由二次多项式生成的条件。

Regularity of joint-meet ideals of distributive lattices

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 consequence, we characterize the distributive lattices $L$ for which the associated Hibi ring has a linear resolution.

On the regularity of join-meet ideals of modular lattices

We study join-meet ideals associated with modular non-distributive lattices. We give a lower bound for the regularity and show that they are not linearly related.