关于Gupta的一个问题

On Gupta's Problem

Ｇｕｐｔａ曾经得到：定理Ａ：若Ｒ是半质环，满足Ｇ（ｎ），Ｇ（＋１）条件，且Ｒ有单位元，则Ｒ是交换环。定理Ｂ：若Ｒ是半质环，满足Ｇ（２）条件，则Ｒ是交换。同时Ｇｕｐｔａ提出如下问题：若Ｒ是半质环，满足Ｇ（ｎ）条件，则Ｒ是否为交换环？本文给出了肯定的回答。

in this Paper we solve the problem that was raised by Gupta. we have obtained: the semipritive ring R stisfed condition G(n) is commutative