A skew polynomial ring over a jacobson ring need not be a jacobson ring

DOI10.1080/00927877708822194zbMath0355.16020OpenAlexW2068201838MaRDI QIDQ4126496

W. Stephenson, K. R. Pearson

Publication date: 1977

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

Full work available at URL: https://doi.org/10.1080/00927877708822194

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Automorphisms and endomorphisms (16W20) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Divisibility, noncommutative UFDs (16U30) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (36)

Some Results On Prime Skew Rings ⋮ Skew polynomials and brown-mccoy rings ⋮ Localization and ideal theory in Noetherian strongly group-graded rings ⋮ Skew polynomial rings over 2-primal rings ⋮ Zero Divisors in Skew Power Series Rings ⋮ On Skew Triangular Matrix Rings ⋮ Radicals of crossed products of enveloping algebras ⋮ Polynomes tordus et t-anneaux a ⋮ Jacobson rings and rings strongly graded by an Abelian group ⋮ On the semiprimitivity of skew polynomial rings ⋮ Some remarks on ore extension rings ⋮ On differential rings and skew pulynomials ⋮ Bootstrapping the bounded nilradical. ⋮ Ore extensions of Jacobson rings. ⋮ Prime factor rings of skew polynomial rings over a commutative Dedekind domain. ⋮ On \(\sigma\)-nil ideals of bounded index of \(\sigma\)-nilpotence. ⋮ Lower bounds on the stable range of skew polynomial rings ⋮ Primeness, semiprimeness and prime radical of ore extensions ⋮ Radicals in skew polynomial and skew Laurent polynomial rings. ⋮ Polynomes tordus a identite polynomiale ⋮ The strongly prime radical of an ore extension ⋮ Descriptions of radicals of skew polynomial and skew Laurent polynomial rings ⋮ Partial Skew Polynomial Rings and Jacobson Rings ⋮ Associative rings ⋮ Prime ideals in skew polynomial rings and quantized Weyl algebras ⋮ Partial Skew Polynomial Rings Over Semisimple Artinian Rings ⋮ Radicals of skew polynomial rings and skew Laurent polynomial rings. ⋮ Prime ideals of graded rings and related matters ⋮ Prime ideals of Ore extensions over commutative rings ⋮ Rigid Ideals and Radicals of Ore Extensions ⋮ On Skew Power Serieswise Armendariz Rings ⋮ On Goldie Prime Ideals of Ore Extensions ⋮ SKEW POLYNOMIAL RINGS WHICH ARE GENERALIZED ASANO PRIME RINGS ⋮ When are all prime ideals in an ore extension goldie? ⋮ Ore extensions and jacobson rings^∗ ⋮ Semiprimeness, quasi-Baerness and prime radical of skew generalized power series rings

Cites Work

• Unnamed Item
• Unnamed Item
• Polynomial extensions of Jacobson rings
• The diamond lemma for ring theory
• Group rings of polycyclic groups
• Hilbert rings and the Hilbert Nullstellensatz
• Radicals Of Polynomial Rings
• Ore Extensions and Polycyclic Group Rings

This page was built for publication: A skew polynomial ring over a jacobson ring need not be a jacobson ring