关于仿射簇的素理想的注记

A Note on the Prime Ideal of an Affine Variety

摘要: 本文研究了一个${\mathbb{A}}^3$ 中的仿射簇，证明了该仿射簇的理想的高度为2，但并不能由2个元素生成。从而说明了仿射簇的素理想并不一定能由其高度个元素生成。

Abstract: This paper studies an affine variety in ${\mathbb{A}}^3$ and proves that the height of its prime ideal is 2, however it cannot be generated by 2 elements. This demonstrates that a prime ideal of an affine variety may not necessarily be generated by a number of elements equal to its height.