Study of blow-up rings

交换代数是代数的一个分支，它研究具有两个二进制运算的集合，例如加法和乘法，例如数的集合和函数的集合。目的是从两个二元操作出发，用视点来探讨这些集合的结构。这是一种非常抽象的方法，但它包含了很好的应用，比如密码学，在现实社会中。我提出了三个具体问题，并一直在努力解决它们。我取得了相当优异的成绩，并在国外的几次会议上作了报告。

Commutative Algebra is one of the branches of algebra, which works on the sets equipped with two binary operations, such that addition and multiplication, such as the sets of numbers and the sets of functions. The purpose is to explore the structure of these sets with view-point from two binary operations. This is a very abstract approach but it contains good applications, like cryptography, to real societies. I have posed three concrete problems and have been trying to solve them. I obtain rather excellent and big results, which I have reported in several conferences of abroad.