Nilpotent polynomials and nilpotent coefficients

DOI10.1016/j.jalgebra.2022.02.024zbMath1496.16020OpenAlexW4221041354MaRDI QIDQ2132475

Thomas L. Draper, Pace P. Nielsen, Janez Šter

Publication date: 28 April 2022

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2022.02.024

zbMATH Keywords

polynomial ringpower series ringnilpotentArmendariz ringzero-divisors

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Ordinary and skew polynomial rings and semigroup rings (16S36) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Conditions on elements (16U99)

Cites Work

• Unnamed Item
• On linearly weak Armendariz rings.
• Amitsur's property for skew polynomials of derivation type
• Nilpotent elements and Armendariz rings.
• The diamond lemma for ring theory
• Armendariz rings
• Polynomial rings over nil rings need not be nil
• McCoy rings and zero-divisors.
• Simplifying Smoktunowicz's Extraordinary Example
• A CONCEPT UNIFYING THE ARMENDARIZ AND NI CONDITIONS
• RINGS OVER WHICH COEFFICIENTS OF NILPOTENT POLYNOMIALS ARE NILPOTENT
• Algebras Over Infinite Fields
• Radicals Of Polynomial Rings
• A note on extensions of Baer and P. P. -rings
• Primeness, semiprimeness and prime radical of ore extensions
• Rings in which nilpotents form a subring
• Rings whose nilpotents form a multiplicative set
• Examples of Armendariz Rings
• Logical connections between some open problems concerning nil rings
• Modules Over Coproducts of Rings

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