Article ID Journal Published Year Pages File Type
4588304 Journal of Algebra 2008 13 Pages PDF
Abstract

We study the structure of the set of nilpotent elements in Armendariz rings and introduce nil-Armendariz as a generalization. We also provide some new examples by proving that if D is a K-algebra and n⩾2, the coproduct D∗KK〈x|xn=0〉 is Armendariz if and only if D is a domain with K∖{0} as its group of units. Finally we study the conditions under which the polynomial ring over a nil-Armendariz ring is nil-Armendariz, which is related to a question of Amitsur.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory