摘要
研究了半交换的π-正则环的扩张.利用环的结构理论,证明了若R是半交换的,I是R的一个理想,则R是π-正则环当且仅当I和R/I都是π-正则环.从而,把Badawi关于有1的半交换的π-正则环的结果推广到了一种更广泛的"半交换环"—半交换的π-正则环(不必含1).半交换的π-正则环类和Abelπ-正则环类也无包含关系.
Extensions of semicommutative w-regular rings are studied using ring structure theory, it is proven that when R is a semicommutative ring, R is a π-regular ring only if I and R/I are π-regular tings for an ideal I of R. Therefore, semicommutative π-regular tings are devoted to generalize results of Badawi on the semicom- mutative w-regular rings with one, and a semicommutative π-ring.
出处
《大连交通大学学报》
CAS
2010年第3期107-108,共2页
Journal of Dalian Jiaotong University
基金
辽宁省"十一五"教育科学规划资助项目
