Radical rings with Engel conditions

DOI10.1006/jabr.2000.8370zbMath0969.16003OpenAlexW2046482056MaRDI QIDQ1584618

Yaroslav P. Sysak, Bernhard Amberg

Publication date: 28 February 2001

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

Full work available at URL: https://semanticscholar.org/paper/18d729b44d814dbd2ae5491cae7fd0ce0913add5

zbMATH Keywords

Engel conditionsadjoint groupsLevitzki radicalJacobson radical ringsLie commutatorsLie multiplication\(n\)-Engel groups\(n\)-Engel rings

Mathematics Subject Classification ID

Center, normalizer (invariant elements) (associative rings and algebras) (16U70) Engel conditions (20F45) Jacobson radical, quasimultiplication (16N20)

Related Items

A 5-Engel associative algebra whose group of units is not 5-Engel ⋮ Radical rings with soluble adjoint groups ⋮ On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation ⋮ Torsion subgroups, solvability and the Engel condition in associative rings ⋮ Group identities on the units of algebraic algebras with applications to restricted enveloping algebras. ⋮ Generating Adjoint Groups ⋮ Behaviour of the Frobenius map in a noncommutative world ⋮ RINGS SATISFYING GENERALIZED ENGEL CONDITIONS ⋮ Engel varieties of associative rings and the number of Mersenne primes

Cites Work

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• The nilpotency of the radical in a finitely generated P.I. ring
• On associative algebras satisfying the Engel condition
• Nonmatrix varieties
• Power closure and the Engel condition
• Engelsche Elemente der Länge drei. (Engel elements of length three.)
• On the adjoint group of some radical rings
• Subgroups of the Adjoint Group of a Radical Ring
• The Centers of a Radical Ring
• Observations on group rings
• Associative rings satisfying the Engel condition
• Algebras with Collapsing Monomials
• On the Adjoint Group of a Radical Ring

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