王湘浩问题及其拟赋值环的相关结果

A PROBLEM OF WANG XIANGHAO AND ITS RELEVANT RESULTS ON QUASI-VALUATION RINGS

一个无零因子的交换环R称为拟赋值环,如果R中有一个非零元素a,使得R的任意非零元都整除a的某个方幂。给出了拟值环的几个相关结果,并在拟赋值环上加上一些限制后,对王湘浩问题作出了肯定的回答。

Let R be a commutative ring without zero-divisor,R is called a quasi-valuation ring,if it contains a non-zero element a such that any non-zero element of R divides a power of a.In this paper,we put up with several conclusions with respective to quasi-valuation ring,and by adding limits to quasi-valuation,we get positive answer of Wang Xianghao problem.