The algebraic hypercenter and some applications

DOI10.1016/0021-8693(83)90127-8zbMath0526.16027OpenAlexW2077492703MaRDI QIDQ594986

Jeffrey Bergen, I. N. Herstein

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0021-8693(83)90127-8

zbMATH Keywords

centercommutativitypolynomial identityalgebraic hypercenteralgebras algebraic over subsetsalgebras without algebraic idealscommutative integral domaincommutativity of algebrashypercenter theoremrings with no nil ideals

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Automorphisms and endomorphisms (16W20) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Center, normalizer (invariant elements) (associative rings and algebras) (16U70) Rings with polynomial identity (16Rxx)

Related Items (6)

On some center-like subsets of rings ⋮ The algebraic hypercenter of an algebra over a commutative ring ⋮ F-algebraic extensions of rings ⋮ A theorem on invariant subrings ⋮ Some results on annihilation in algebras ⋮ Annihilators in rings with involution

Cites Work

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• A theorem on invariant subrings
• Rings radical over P. I. subrings
• A commutativity theorem for rings with derivations
• On the hypercenter of a ring
• General polynomial identities. II
• Invariant subrings of a certain kind
• Prime rings satisfying a generalized polynomial identity
• A Theorem Concerning Three Fields
• Radical Extensions of Rings
• Some results on the center of a ring with polynomial identity
• On a theorem of H. Cartan
• A commutativity theorem

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