逆字典序Gröbner基与强Koszul环面环
Reverse lexicographic Gröbner bases and strongly Koszul toric rings
摘要：
Restuccia和Rinaldo证明了标准分次$K$ -代数$K[x_1, ... x_n]/I$是强Koszul的，如果$I$关于任何逆字典序的约化Gröbner基是二次的.本文利用环面理想$I_A$的逆字典序Gröbner基给出环面环$K[A]$是强Koszul的一个充分条件.这是Restuccia和Rinaldo给出的一个结果的部分推广。此外，我们还证明了任何由无平方单项式生成的强Koszul环面环都是压缩的。利用这一事实，我们证明了当$K[A]$是由无平方单项式生成时，我们的充分条件$K[A]$是强Koszul的充要条件.
英文摘要：
Restuccia and Rinaldo proved that a standard graded $K$-algebra $K[x_1, ... x_n]/I$ is strongly Koszul if the reduced Gröbner basis of $I$ with respect to any reverse lexicographic order is quadratic. In this paper, we give a sufficient condition for a toric ring $K[A]$ to be strongly Koszul in terms of the reverse lexicographic Gröbner bases of its toric ideal $I_A$. This is a partial extension of a result given by Restuccia and Rinaldo. In addition, we show that any strongly Koszul toric ring generated by squarefree monomials is compressed. Using this fact, we show that our sufficient condition for $K[A]$ to be strongly Koszul is both necessary and sufficient when $K[A]$ is generated by squarefree monomials.
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