Krull交定理的一个初等证明

An elementary proof of Krull intersection theorem

Krull交定理是交换代数中的一个重要定理,有着广泛的应用。针对交换代数书上的证明比较深奥,学生难以理解,本文应用Hilbert基定理,给出一个能够揭示其本质的简单证明,同时给出一个推论。

Krull intersection theorem is an important theorem in commutative algebra, it has a wide range of applications. However, the proof on commutative algebra books is profound, and it is very difficult for student to understand. In this paper, a simple proof is used to reveal its nature by applying the well-known Hilbert Basis Theorem, and a corollary is given.