| 摘要: |
| 证明R是V-环(或GV-环;FS-环;IF-环;FC-环;n-FC环)当且仅当S和T都是V-环(或GV-环;FS-环;IF-环;FC-环;n-FC环),其中S和T是环,R=S⊕T.一般地,当R=⊕i=1m Ri时,类似的结论也成立. |
| 关键词: V-环 GV-环 FS-环 IF-环 FC-环 n-FC 环 |
| DOI： |
| 投稿时间：2012-02-13修订日期：2012-06-15 |
| 基金项目:广西教育厅科研项目(N0.201203YB224)资助。 |
|
| Finite Direct Sums of Some Rings |
|
DUAN Lu-ling
|
| (Department of Mathematics and Computer Science, Guangxi College of Education, Nanning, Guangxi, 530023, China) |
| Abstract: |
| Let S and T be rings, R=S⊕T.We proved that R is a V-ring (resp., GV-ring;FS-ring;IF-ring;FC-ring;n-FC ring) if and only if both S and T are V-ring (resp., GV-ring;FS-ring;IF-ring;FC-ring;n-FC ring).In general, let R1, R2, …, Rm be rings.We obtained that ⊕i=1m Ri is a V-ring (resp., GV-ring;FS-ring;IF-ring;FC-ring;n-FC ring)if and only if each Ri is a V-ring (resp., GV-ring;FS-ring;IF-ring;FC-ring;n-FC ring). |
| Key words: V-ring GV-ring FS-ring IF-ring FC-ring n-FC ring |
