零維 Gorenstein 理想

Abstract

在這篇論文裡,我們討論了兩個關於Gorenstein Ideals的問題:在第2節裡,我們找出了 (x_{1}^{n},x_{2}^{n},...,x_{s}^{n},y_{1}^{n},...,y_{t}^{n}): x_{1}^{alpha_{1}}x_{2}^{alpha_{2}}cdots x_{s}^{alpha_{s}} y_{1}^{ eta_{1}}y_{2}^{ eta_{2}}... y_{t}^{ eta_{t}}(x_{1}^{gamma_{1}} x_{2}^{gamma_{2}}cdots x_{s}^{gamma_{s}}-y_{1}^{delta_{1}} y_{2}^{delta_{2}}cdots y_{t}^{delta_{t}}) 的所有生成元。在第3節,我們解決了(x^{n},y^{n},z^{n}):x+y+z 的生成個數。 在第3節的證明中我們需要證明一個在二項式係數下的矩陣是非奇異的。在第4節中, 我們解決了這個問題。

In this paper, we solve two problem of Gorenstein Ideals :In section 2, we find the generators of the ideal ((x_{1}^{n},x_{2}^{n},...,x_{s}^{n},y_{1}^{n},...,y_{t}^{n}): x_{1}^{alpha_{1}}x_{2}^{alpha_{2}}cdots x_{s}^{alpha_{s}} y_{1}^{ eta_{1}}y_{2}^{ eta_{2}}... y_{t}^{ eta_{t}}(x_{1}^{gamma_{1}} x_{2}^{gamma_{2}}... x_{s}^{gamma_{s}}-y_{1}^{delta_{1}} y_{2}^{delta_{2}}... y_{t}^{delta_{t}})). In section 3, we find the number of generators of ((x^{n},y^{n},z^{n}):x+y+z). In the proof of section 3, we need to show that a matrix on binomial coefficients is nonsigular. We solve this problem in section 4.