A unified approach to the armendariz property of polynomial rings and power series rings
Journal
Colloquium Mathematicum
Journal Volume
113
Journal Issue
1
Pages
119-149
Date Issued
2008
Author(s)
Zhou, Y.
Abstract
A ring R is called Armendariz (resp., Armendariz of power series type) if, whenever (Formula presented) for all i and j. This paper deals with a unified generalization of the two concepts (see Definition 2). Some known results on Armendariz rings are extended to this more general situation and new results are obtained as consequences. For instance, it is proved that a ring R is Armendariz of power series type iff the same is true of R[[x]]. For an injective endomorphism σ of a ring R and for n ≥ 2, it is proved that R[x σ]/(xn) is Armendariz iff it is Armendariz of power series type iff σ is rigid in the sense of Krempa.
Type
journal article