关于$\pi$-半交换环

On $\pi$-Semicommutative Rings

中文关键词:  半交换环  左GWZI环  $\pi$-半交换环

英文关键词:semicommutative rings  left GWZI rings  $\pi$-semicommutative rings

中文摘要:

      环$R$称为$\pi$-半交换的,如果对于$a,b\in R$,条件$ab=0$蕴含存在正整数$n$使得$a^nRb^n=0$.我们研究了$\pi$-半交换环的性质以及这类环与其它相关环类的关系.特别地,我们否定地回答了关于左GWZI环的一个问题.

英文摘要:

      A ring $R$ is said to be $\pi$-semicommutative if $a,b\in R$ satisfy $ab=0$ then there exists a positive integer $n$ such that $a^nRb^n=0$. We study the properties of $\pi$-semicommutative rings and the relationship between such rings and other related rings. In particular, we answer a question on left GWZI rings negatively.