中文摘要：

本文用一种新的方法研究了有关一维Noether环的一个不等式．通过用重数替换长度进一步地把该不等式推广到二维的情形．

英文摘要：

In this paper, we study a well-known inequality on Noether rings with one dimension by another method. We will replace the length function with the multiplicity; thus we can rewrite the inequality and extend the inequality to rings with dimension more than one.