Jacobson Radicals of Ore Extensions of Derivation Type

DOI10.1080/00927870601117613zbMath1132.16023OpenAlexW2126626325MaRDI QIDQ3435937

Chen-Lian Chuang, Yuan-Tsung Tsai, Tsu-Yang Wu

Publication date: 8 May 2007

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

Full work available at URL: http://ntur.lib.ntu.edu.tw/bitstream/246246/184019/1/06.pdf

zbMATH Keywords

Jacobson radicalpolynomial identitiessemi-prime ringschain conditionsOre extensionsnil radicalquasi-algebraic derivations

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Prime and semiprime associative rings (16N60) Derivations, actions of Lie algebras (16W25) Jacobson radical, quasimultiplication (16N20)

Related Items (15)

How far can we go with Amitsur's theorem in differential polynomial rings? ⋮ Locally nilpotent skew extensions of rings ⋮ Differential polynomial rings over locally nilpotent rings need not be Jacobson radical. ⋮ Jacobson radicals of ring extensions. ⋮ Differential polynomial rings over rings satisfying a polynomial identity. ⋮ Quasi-duo differential polynomial rings ⋮ Higher derivations of Ore extensions by \(q\)-skew derivations. ⋮ Symmetric Utumi quotient rings of Ore extensions by skew derivations ⋮ Higher derivations of Ore extensions. ⋮ On the Jacobson Radical of Skew Polynomial Extensions of Rings Satisfying a Polynomial Identity ⋮ On the semiprimitivity of free skew extensions of rings ⋮ Smash products and differential identities ⋮ Symmetric Martindale Quotient Rings of Ore Extensions with More than One Indeterminate ⋮ On the structure of semi-invariant polynomials in Ore extensions. ⋮ Radicals in differential polynomial rings

Cites Work

• Semiprime rings with prime ideals invariant under derivations.
• Differential identities of semiprime rings
• The extended centroid and \(X\)-inner automorphisms of Ore extensions
• On Radicals of Skew Polynomial Rings of Derivation Type
• A note on semiprimitivity of ore extensions

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