论文标题
在相关的半群代数的渐变环上
On the Associated Graded ring of Semigroup Algebras
论文作者
论文摘要
在本文中，我们为使用gröbner的简单仿射半群的相关分级环提供了必要的条件。我们概括了简单仿射半群的均匀数值半群的概念，并表明相应的半群环的贝蒂数与相关分级环的贝蒂数匹配。我们还为简单的仿射半群定义了不错的扩展，这是由数值半群的良好扩展的概念所激发的。
In this paper, we give the necessary and sufficient conditions for the Cohen-Macaulayness of the associated graded ring of a simplicial affine semigroups using Gröbner basis. We generalize the concept of homogeneous numerical semigroup for the simplicial affine semigroup and show that the Betti numbers of the corresponding semigroup ring matches with the Betti numbers of the associated graded ring. We also define the nice extension for simplicial affine semigroups, motivated by the notion of a nice extension of the numerical semigroups.
