弱Armendariz环与半群环  

Weak Armendariz rings and semigroup rings

作　　者：何建伟[1] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《纺织高校基础科学学报》2007年第1期64-67,共4页Basic Sciences Journal of Textile Universities

摘　　要：把弱Armendariz环的概念推广得到S-弱Armendariz环,讨论了一个环R是S-弱Armen-dariz环的充要条件.进而,得到了R是S×T-弱Armendariz环当且仅当R既是S-弱Armendari环又是T-弱Armendariz环.最后,得到R1×R2是S-弱Armendariz环当且仅当R1和R2均为S-弱Armendariz环.A semigroup S, S-weak Armendariz rings are introduced , which are generaligations of weak Armendariz rings. A necessary and sufficient condition for a ring to be S-weak Armendariz is obtained. Consequently, it is shown that R is S×T-weak Armendariz if and only if R is both S-weak Armendariz and T-weak Armendariz. Finally, it is shown that R1×R2 is S-weak Armendariz if and only if both R1 and R2 are S-weak Armendariz.

关 键 词：弱ARMENDARIZ环 半群环 S-弱Armendariz环 

分 类 号：O153.3[理学—数学]