Integrality for PI-rings

DOI10.1016/0021-8693(92)90131-5zbMath0770.16011OpenAlexW1987434726MaRDI QIDQ1204551

Nikolaus Vonessen, Amiram Braun

Publication date: 29 March 1993

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

Full work available at URL: https://doi.org/10.1016/0021-8693(92)90131-5

zbMATH Keywords

centerincomparabilityactionsclassical Krull dimensionPI-algebrasintegralityPI-ringsintegral extensionstrace ringlying overgoing upaffine PI-algebrasembeddings of quotient ringsintegral centralizing extensionsmodule-finitenessSchelter integrality

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Trace rings and invariant theory (associative rings and algebras) (16R30) Conditions on elements (16U99) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Ideals in associative algebras (16D25) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Units, groups of units (associative rings and algebras) (16U60) Noetherian rings and modules (associative rings and algebras) (16P40) Centralizing and normalizing extensions (16S20)

Related Items

Invariants of the action of a semisimple Hopf algebra on PI-algebra ⋮ Factorial properties of the enveloping algebra of a nilpotent Lie algebra in prime characteristic ⋮ Unions of chains of primes ⋮ On bimodules over Noetherian PI rings ⋮ Determinants, integrality and Noether's theorem for quantum commutative algebras ⋮ Actions of Linearly Reductive Groups on Pi-Algebras

Cites Work

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• Integrality and prime ideals in fixed rings of P.I. rings
• Smash products, inner actions and quotient rings
• Integrality and normalizing extensions of rings
• Integral ring homomorphisms
• Finite extensions are integral
• Subrings of Artinian and Noetherian rings
• P.I. degrees and prime ideals
• Prime ideals in finite extensions of Noetherian rings
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• Fixed point rings of some non noetherian rings
• Some Remarks on Affine Rings
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• A Note on Noetherian P.I. Rings
• Prime Ideals in Intermediate Extensions
• Finite Correspondence of Spectra in Noetherian Ring Extensions
• A Characterization of Prime Noetherian P.I. Rings and a Theorem of Mori- Nagata
• Integrality Over Fixed Rings
• Trace-Like Functions on Rings with no Nilpotent Elements
• Krull dimension
• Prime ideals in intermediate integral centralizing extensions of PI-rings