湖州师范学院学报
湖州師範學院學報
호주사범학원학보
JOURNAL OF HUZHOU TEACHERS COLLEGE
2011年
2期
26-29
,共4页
斜多项式环%3-Armendariz环%(α,3)-Armendafiz环
斜多項式環%3-Armendariz環%(α,3)-Armendafiz環
사다항식배%3-Armendariz배%(α,3)-Armendafiz배
Skew polynomial ring%3-Armendariz ring%(α,3)-Armendariz ring
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)-Armendafiz环.列举了一些例子和反例.
設α是環R的一箇自同態,引入瞭(α,3)-Armendariz環的概唸,它是3-Armendariz環和α-Armendariz環概唸的推廣,證明瞭若R是域且α是環R的任意單同態,則R是(α,3)-Armendariz環.R是(α,3)-Armendariz環噹且僅噹Ra是(α,3)-Armendafiz環.列舉瞭一些例子和反例.
설α시배R적일개자동태,인입료(α,3)-Armendariz배적개념,타시3-Armendariz배화α-Armendariz배개념적추엄,증명료약R시역차α시배R적임의단동태,칙R시(α,3)-Armendariz배.R시(α,3)-Armendariz배당차부당Ra시(α,3)-Armendafiz배.열거료일사례자화반례.
For an endomorphism α of a ring R,we introduce(α,3)-Armendariz rings,which are generalizations of 3-Armendafiz tings 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 ex-amples and counterexamples are included for answers to questions that occur naturally in the process of this case.
