论文标题
Noetherian本地戒指的一些新的不变性与最大理想的平方有关
Some new invariants of Noetherian local rings related to square of the maximal ideal
论文作者
论文摘要
我们介绍了两个新的不变式（标准分级）本地环$（R，\ Mathfrak M）$，它们测量了某些减少$ \ Mathfrak M，$的发电机数量，我们研究了它们的属性。明确地，我们考虑了理想的发电机数量$ i $的最小值，以便$ i^2 = \ mathfrak m^2 $或$ i \ supseteq \ supseteq \ mathfrak m^2 $保持。随后，我们研究了$ r $是由均质二次形式产生的理想$ i $的多项式环$ k [x_1，\ dots，x_n] $的商，我们计算这些不变性。我们将特定的注意力集中在$ r $的情况下是多项式环$ k [x_1，\ dots，x_n] $ by Edge the Edge the有限简单图$G。$。
We introduce two new invariants of a Noetherian (standard graded) local ring $(R, \mathfrak m)$ that measure the number of generators of certain kinds of reductions of $\mathfrak m,$ and we study their properties. Explicitly, we consider the minimum among the number of generators of ideals $I$ such that either $I^2 = \mathfrak m^2$ or $I \supseteq \mathfrak m^2$ holds. We investigate subsequently the case that $R$ is the quotient of a polynomial ring $k[x_1, \dots, x_n]$ by an ideal $I$ generated by homogeneous quadratic forms, and we compute these invariants. We devote specific attention to the case that $R$ is the quotient of a polynomial ring $k[x_1, \dots, x_n]$ by the edge ideal of a finite simple graph $G.$
