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.
出处
《数学进展》
CSCD
北大核心
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)
