Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588304 | Journal of Algebra | 2008 | 13 Pages |
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.
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Physical Sciences and Engineering
Mathematics
Algebra and Number Theory