Associative rings with metabelian adjoint group.

DOI10.1016/j.jalgebra.2004.02.028zbMath1062.16028OpenAlexW2031750912MaRDI QIDQ1882871

Bernhard Amberg, Yaroslav P. Sysak

Publication date: 1 October 2004

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.02.028

zbMATH Keywords

Jacobson radicallocal ringsadjoint groupsradical ringsresidually finite ringsmetabelian groupsLie ringsassociative ringssubdirectly irreducible ringsmultiplicative groups of ringsArtin-Rees property of idealscommutator ideals of ringsLie metabelian ringsresidually nilpotent ringsrings of generalized quotientsweakly Noetherian rings

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Jacobson radical, quasimultiplication (16N20) Units, groups of units (associative rings and algebras) (16U60)

Related Items (5)

A 5-Engel associative algebra whose group of units is not 5-Engel ⋮ Torsion subgroups, solvability and the Engel condition in associative rings ⋮ Semilocal rings whose adjoint group is locally supersoluble. ⋮ The complete matrix ring over an adjoint regular ring is adjoint regular. ⋮ Generating Adjoint Groups

Cites Work

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• Lie centrally metabelian group rings
• Über Ringe mit Kommutatorbeziehungen
• Radical rings with soluble adjoint groups
• Complex analysis and convolution operators
• Lie Solvable Rings
• On rings whose associated Lie rings are nilpotent
• The Splitting of Certain Solvable Groups
• Associative rings whose adjoint semigroup is locally nilpotent

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