On Lie Nilpotent Rings and Cohen's Theorem

DOI10.1080/00927872.2014.952735zbMath1333.16003arXiv1501.00787OpenAlexW2963534752MaRDI QIDQ3448542

Jenő Szigeti, Leon van Wyk

Publication date: 26 October 2015

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

Full work available at URL: https://arxiv.org/abs/1501.00787

zbMATH Keywords

nilpotent elementsleft idealsnilpotent idealstwo-sided idealsfinitely generated idealsprime radicalcompletely prime idealsLie centerLie nilpotent ringsCohen theoremtwo-sided nil ideals

Mathematics Subject Classification ID

Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Generalizations of commutativity (associative rings and algebras) (16U80) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Ideals in associative algebras (16D25) Center, normalizer (invariant elements) (associative rings and algebras) (16U70) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items

Lie solvability and the identity \([x_{1},y_{1}[x_{2},y_{2}]\cdots[x_{q},y_{q}]=0\) in certain matrix algebras] ⋮ Torsion subgroups, solvability and the Engel condition in associative rings ⋮ The maximum dimension of a Lie nilpotent subalgebra of $\boldsymbol {\mathbb {M}_n(F)}$ of index $\boldsymbol {m}$ ⋮ A power Cayley-Hamilton identity for \(n \times n\) matrices over a Lie nilpotent ring of index \(k\)

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