Jacobson radicals of ring extensions.

DOI10.1016/j.jpaa.2012.03.023zbMath1267.16019OpenAlexW2060166235MaRDI QIDQ1940193

Jeffrey Bergen, Piotr Grzeszczuk

Publication date: 6 March 2013

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2012.03.023

zbMATH Keywords

locally nilpotent derivationsJacobson radicalrings of constantsskew derivationsacc on right annihilatorsnormalizing elementsright annihilators of powersskew polynomial rings of derivation type

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) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Jacobson radical, quasimultiplication (16N20) Centralizing and normalizing extensions (16S20)

Related Items (11)

How far can we go with Amitsur's theorem in differential polynomial rings? ⋮ On NI and NJ skew PBW extensions ⋮ Locally nilpotent skew extensions of rings ⋮ Differential polynomial rings over locally nilpotent rings need not be Jacobson radical. ⋮ Differential polynomial rings over rings satisfying a polynomial identity. ⋮ Radicals of Skew Polynomial and Skew Laurent Polynomial Rings Over Skew Armendariz Rings ⋮ Factorizations for difference operators ⋮ On the Jacobson Radical of Skew Polynomial Extensions of Rings Satisfying a Polynomial Identity ⋮ On the semiprimitivity of free skew extensions of rings ⋮ A simple solution of the ADS-problem ⋮ Radicals in differential polynomial rings

Cites Work

• Radicals of crossed products of enveloping algebras
• Jacobson radical of skew polynomial rings and skew group rings
• On Rings with Locally Nilpotent Skew Derivations
• GOLDIE DIMENSION OF CONSTANTS OF LOCALLY NILPOTENT SKEW DERIVATIONS
• Radicals Of Polynomial Rings
• Jacobson Radicals of Ore Extensions of Derivation Type
• Rings with Fixed-Point-Free Group Actions

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