半交换环的一个推广研究

On a Generalization of Semicommutative Rings

中文关键词:  半交换环  GWZI环  平凡扩张.

英文关键词:semicommutative rings  GWZI rings  trivial extension.

中文摘要:

      本文研究了半交换环的一种推广. 环$R$称为左GWZI环,如果对环$R$中任意元素$a$, $l(a)$是环$R$的 GW-环. 我们证明了环$R$是左GWZI环当且仅当$S_{3}(R)$是GWZI环于$2$的自然数$n$, $V_{n}(R)$是GWZI环.当且仅当对任意大于等

英文摘要:

      In this paper, a generalization of the class of semicommutative rings is investigated. A ring $R$ is called left GWZI if for any $a \in R$, $l(a)$ is a GW-ideal of $R$. We prove that a ring $R$ is left GWZI if and only if $S_{3}(R)$ is left GWZI if and only if $V_{n}(R)$ is left GWZI for any $n\geq2$.