论文标题
晶体模块的最小自由分辨率
Minimal free resolution of Crystal module
论文作者
论文摘要
山高木·希比（Takayuki Hibi）于1987年引入了联盟赛理想。这是由有限晶格定义的二项式理想。我们研究并不总是满足模块化的非分配有限晶格的联盟理想。特别是，我们处理的是水晶晶格的情况下之一。它是由Yohei Oshida于2022年引入的。标题中的晶体模块是残基类环，与Crystal Grattice的联接赛理想有关。在本文中，我们对晶体模块的最小自由分辨率产生了重要的不平等。关于此结果的重要一点是，可以使用Koszul复合物评估晶体模块的投射维度和贝蒂数字。
The join-meet ideal was introduced by Takayuki Hibi in 1987. It is binomial ideals that are defined by finite lattices. We study the join-meet ideal of non-distributive finite lattices that do not always satisfy modular. In particular, we work on the case of Crystal lattice which is one of them. It was introduced by Yohei Oshida in 2022. The Crystal module in the title is the residue class ring which is in relation to the join-meet ideal of Crystal lattice. In this paper, we give important inequalities about the minimal free resolution of the Crystal module. The important point about this result is that the projective dimension and Betti-number of the Crystal module can be evaluated by using the Koszul complex.
