Armendariz rings and gaussian rings
Armendariz rings and gaussian rings
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DOI：
10.1080/00927879808826274
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发表时间：
1998
影响因子：
0.7
通讯作者：
D. D. Anderson-D.;V. Camillo
中科院分区：
文献类型：
--
作者：
D. D. Anderson-D.;V. Camillo
我们证明了有关Armendariz环和高斯环的一些结果。回想一下，（交换）环R是（高斯）Armendariz，如果对于两个多项式f，g∈R[X]（由f g的系数生成的R的理想是由f和g的系数生成的理想的乘积）fg = 0意味着对于f的每个系数ai和g的每个系数B j，ai B j=0。一些例子的Armendariz环。我们证明了R Armendariz蕴涵R[X]是Armendariz，并且对于R vonNeumann regularR是Armendariz当且仅当R是约化的。我们证明了R是高斯的当且仅当R的每个同态像是Armendariz。给出了R[X]和R[X]为高斯分布时的特征。
We prove a number of results concerning Armendariz rings and Gaussian rings. Recall that a (commutative) ring R is (Gaussian) Armendariz if for two polynomials f,g∈R[X] (the ideal of R generated by the coefficients of f g is the product of the ideals generated by the coefficients of f and g) fg = 0 implies a i b j=0 for each coefficient a i of f and b j of g. A number of examples of Armendariz rings are given. We show that R Armendariz implies that R[X] is Armendariz and that for R von Neumann regularR is Armendariz if and only if R is reduced. We show that R is Gaussian if and only if each homomorphic image of R is Armendariz. Characterizations of when R[X] and R[X] are Gaussian are given.