关于亚直既约环为体的条件  

CONDITIONS THAT A SUBDIRECTLY IRREDUCIBLE RING IS A DIVISION RING

作　　者：孙建华 

机构地区：[1]扬州师院数学系

出　　处：《扬州师院学报（自然科学版）》1990年第3期21-24,共4页

摘　　要：证明了亚直既约环R为体的充要条件是R的心不含非零幂零元,且R的含于心内的主左理想具有降链条件,得到了交换的亚直既约环为域的充要条件为R的心是幂等的,此外还证明了心为强正则的亚直既约环为体。We prove that a subdirectly irreducible ring R is a division ring if and only if the heart H of R has no any nonzero nilpotent element, and the principal left ideals of R contained in H satisfy the descending chain condition. We obtain that a subdirectly irreducible commutative ring R is a field if and only if the heart H of R is idempotent, or if and only if H does not contain a nonzero nilpotent element, or if and only if H does not contain a right or left zero divisor in R. We also prove that if the heart H of subdirectly irreducible ring R is strongly regular then R is a division ring.

关 键 词：亚直既约环 主左理想 强正则 

分 类 号：O153.3[理学—数学]