关于(α,3)-Armendariz环(英文)

ON(α,3)-Armendariz Rings

设α是环R的一个自同态,引入了(α,3)-Armendariz环的概念,它是3-Armendariz环和α-Armendariz环概念的推广,证明了若R是域且α是环R的任意单同态,则R是(α,3)-Armendariz环.R是(α,3)-Armendariz环当且仅当Ra是(α,3)-Armendariz环.列举了一些例子和反例.

For an endomorphism α of a ring R,we introduce（α,3）-Armendariz rings,which are generalizations of 3-Armendariz rings and α-Armendariz rings;prove that if R be a domain,then R is an（α,3）-Armendariz ring for any monomorphism α of R;show that R is an（α,3）-Armendariz ring if and only if so is Ra.Moreover,several examples and counterexamples are included for answers to questions that occur naturally in the process of this case