McCoy环的Ore扩张(英文)  

Ore Extensions of McCoy Rings

作　　者：欧阳伦群[1,2] 陈焕银[2] 

机构地区：[1]湖南科技大学数学与计算科学学院,湘潭湖南411201 [2]湖南师范大学数学与计算科学学院,长沙湖南410006

出　　处：《数学进展》2010年第3期289-296,共8页Advances in Mathematics（China）

基　　金：supported by Scientific Research Fund of Hunan Provincial Education Department (No.07c268);Hunan Province Natural Science Foundation of China(No.06jj20053);Scientific Research Fund of Hunan Province Education Department(No.06A017)

摘　　要：本文研究了斜多项式环与微分多项式环的McCoy性质,证明了如果环R是α-compatible和可逆的,那么斜多项式R[x;α]是McCoy环当且仅当环R是McCoy环;同时我们也证明了如果环R是δ-compatible与可逆的,那么微分多项式环R[x;δ]是McCoy环当且仅当环R是McCoy环.因此本文对McCoy环的相关结论进行了推广.In this paper we study the property.McCoy of skew polynomial rings and differential polynomial rings,and it is shown that if R isα-compatible and reversible,then R[x,α]is McCoy if and only if R is McCoy.Also we prove that if R isδ-compatible and reversible,then R[x,δ]is McCoy if and only if R is McCoy.Consequently,several known results on McCoy rings are extended to a general setting.

关 键 词：McCoy环 可逆环 多项式扩张 

分 类 号：O153.3[理学—数学]