广义弱Armendariz环及其扩张(英文)  

Generalized Weak Armendariz Rings and Their Extensions

作　　者：赵良[1] 

机构地区：[1]安徽工业大学数理学院,马鞍山安徽243032

出　　处：《数学进展》2015年第2期175-186,共12页Advances in Mathematics（China）

基　　金：Supported by the Provincial Natural Science Research Program of Higher Education Institution of Anhui Province of China(No.KJ2012Z028)

摘　　要：对环R的一个自同态α,通过引入α-弱Armendariz环和α-弱拟Armendariz环研究了R相对于α的弱Armendariz性质.这两类环是对弱Armendariz环和弱拟Armendariz环的进一步推广,为研究环的弱Armendariz性质提供了新思路.本文对这两类环给出了一些刻画,构造了一些所需的例子和反例,统一和推广了一些已知的研究结果.For an endomorphism a of a ring R,we introduce the concepts of a-weak Armendariz rings and a-weak quasi-Armendariz rings to investigate the relative weak Armendariz properties relative to a in a general setting.The two new classes of rings extend the classes of weak Armendariz rings and weak quasi-Armendariz rings respectively,and thus we can study various weak Armendariz properties of a ring from a new perspective.Characterizations of α-weak Armendariz rings and α-weak quasi-Armendariz rings are given,and some examples and counter-examples needed in the process are also constructed.Some known results are unified and generalized.

关 键 词：弱ARMENDARIZ环 弱拟Armendariz环 α-弱Armendariz环 α-弱拟Armendariz环 α-弱McCoy模 

分 类 号：O153.3[理学—数学]