Centralizing maps on invertible or singular matrices over division rings.

DOI10.1016/j.laa.2013.10.016zbMath1294.16030OpenAlexW2007255176MaRDI QIDQ2442239

Cheng-Kai Liu

Publication date: 2 April 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2013.10.016

zbMATH Keywords

invertible matricessingular matricesrings of matricesfunctional identitiesdivision ringsadditive mapscentralizing maps

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Automorphisms and endomorphisms (16W20) Commutativity of matrices (15A27) Linear preserver problems (15A86) Functional identities (associative rings and algebras) (16R60)

Related Items (21)

Nonadditive strong commutativity preserving maps on rank-k matrices over division rings ⋮ Unnamed Item ⋮ Centralizing traces and Lie triple isomorphisms on generalized matrix algebras ⋮ On centralizing additive maps on rank one triangular matrices over division rings ⋮ Commuting maps on strictly upper triangular matrix rings ⋮ Weakly commuting maps on the set of rank-1 matrices ⋮ Additive maps on rank-smatrices ⋮ Unnamed Item ⋮ Additive maps of rankrtensors and symmetric tensors ⋮ Commuting maps on rank k triangular matrices ⋮ Central traces of multiadditive maps on invertible matrices ⋮ Centralizing traces with automorphisms on triangular algebras ⋮ Maps determined by rank-\(s\) matrices for relatively small \(s\) ⋮ Additive maps on invertible matrices ⋮ Power commuting additive maps on invertible or singular matrices ⋮ Power commuting additive maps on rank-klinear transformations ⋮ Centralizing additive maps on rank r block triangular matrices ⋮ Centralizing traces and Lie-type isomorphisms on generalized matrix algebras: a new perspective ⋮ Power commuting traces of bilinear maps on invertible elements ⋮ Commuting maps on invertible triangular matrices over \(\mathbb{F}_2\) ⋮ An Engel condition with b-generalized derivations for Lie ideals

Cites Work

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• AN APPLICATION OF LOCAL MULTIPLIERS TO CENTRALIZING MAPPINGS OF C^*-ALGEBRAS
• Linear identities and commuting maps in rings with involution
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