Differential polynomial rings over locally nilpotent rings need not be Jacobson radical.

DOI10.1016/j.jalgebra.2014.04.022zbMath1303.16024arXiv1311.3571OpenAlexW2069002742MaRDI QIDQ403607

Michał Ziembowski, Agata Smoktunowicz

Publication date: 29 August 2014

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

Full work available at URL: https://arxiv.org/abs/1311.3571

zbMATH Keywords

skew polynomial ringslocally nilpotent derivationsJacobson radicalskew polynomial extensionslocally nilpotent rings

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Derivations, actions of Lie algebras (16W25) Jacobson radical, quasimultiplication (16N20)

Related Items (13)

On differential polynomial rings over locally nilpotent rings ⋮ How far can we go with Amitsur's theorem in differential polynomial rings? ⋮ Locally nilpotent skew extensions of rings ⋮ ON THE CONNECTION BETWEEN DIFFERENTIAL POLYNOMIAL RINGS AND POLYNOMIAL RINGS OVER NIL RINGS ⋮ Differential polynomial rings over rings satisfying a polynomial identity. ⋮ On differential polynomial rings over nil algebras ⋮ On skew polynomial rings over locally nilpotent rings ⋮ Irreducible bimodules over alternative algebras and superalgebras ⋮ Differential polynomial rings in several variables over locally nilpotent rings ⋮ On the semiprimitivity of free skew extensions of rings ⋮ Iterated differential polynomial rings over locally nilpotent rings ⋮ Derivations and bounded nilpotence index ⋮ Radicals in differential polynomial rings

Cites Work

• Jacobson radicals of ring extensions.
• On differential rings and skew pulynomials
• Radicals Of Polynomial Rings
• Jacobson Radicals of Ore Extensions of Derivation Type
• On Radicals of Skew Polynomial Rings of Derivation Type
• Noetherian Ore Extensions and Jacobson Rings
• The Jacobson radical of rings with nilpotent homogeneous elements

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