Elsevier

Journal of Algebra

Volume 319, Issue 8, 15 April 2008, Pages 3128-3140
Journal of Algebra

Nilpotent elements and Armendariz rings

https://doi.org/10.1016/j.jalgebra.2008.01.019Get rights and content
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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 n2, the coproduct DKKx|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.

Keywords

Armendariz ring
Nil-Armendariz ring
Polynomial ring
Nilpotent elements

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Work supported by MEC-DGESIC (Spain) through grant MTM2005-00934B, and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya through grant 2005SGR00206.