On maps preserving zeros of Lie polynomials of small degrees (Q1044536)
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scientific article; zbMATH DE number 5649988
| Language | Label | Description | Also known as |
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| English | On maps preserving zeros of Lie polynomials of small degrees |
scientific article; zbMATH DE number 5649988 |
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On maps preserving zeros of Lie polynomials of small degrees (English)
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18 December 2009
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A Lie polynomial is an element of the free algebra generated by some set of variables. In this note, the authors describe maps preserving zeros of multilinear Lie polynomials of degrees \(3\) and \(4\) on prime algebras and matrices over unital algebras. The main techniques are based on functional identities developed by \textit{M. Brešar} [Trans. Am. Math. Soc. 335, No.~2, 525--546 (1993; Zbl 0791.16028) and Isr. J. Math. 162, 317--334 (2007; Zbl 1142.16020)].
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linear preserver problems
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zeros of Lie polynomials
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prime rings
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multilinear Lie polynomials
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prime algebras
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unital algebras
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