Commutators and images of noncommutative polynomials

DOI10.1016/j.aim.2020.107346zbMath1459.16022arXiv2001.10392OpenAlexW3047764774MaRDI QIDQ2006071

Matej Brešar

Publication date: 8 October 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.10392

zbMATH Keywords

matrix algebraWaring's problemcommutatornoncommutative polynomialpolynomial identityLie ideallocally linearly dependent polynomialssquare-zero element

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) General theory of (C^*)-algebras (46L05) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Functional identities (associative rings and algebras) (16R60)

Related Items

On n-generalized commutators and Lie ideals of rings, On the subring generated by commutators, Additive subgroups generated by noncommutative polynomials, Evaluations of multilinear polynomials on low rank Jordan algebras, Values of polynomials on centrally closed prime algebras, Images of multilinear graded polynomials on upper triangular matrix algebras, The Waring problem for matrix algebras, II, Functional identities and their applications, The images of multilinear and semihomogeneous polynomials on the algebra of octonions, Multilinear polynomials are surjective on algebras with surjective inner derivations, The Waring problem for matrix algebras, Evaluations of noncommutative polynomials on algebras: methods and problems, and the L'vov-Kaplansky conjecture, On the images of generalized polynomials evaluated on matrices over an algebraically closed skew field, Images of multilinear polynomials in the algebra of finitary matrices contain trace zero matrices, On Fagundes-Mello conjecture, Noncommutative higher commutators

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