Images of multilinear polynomials in the algebra of finitary matrices contain trace zero matrices
| Autor: | Daniel Vitas |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Multilinear map Algebra and Number Theory Infinite field Trace (linear algebra) Image (category theory) 010102 general mathematics Zero (complex analysis) Mathematics - Rings and Algebras 010103 numerical & computational mathematics 16R99 16W25 01 natural sciences Algebra Integer Rings and Algebras (math.RA) FOS: Mathematics Discrete Mathematics and Combinatorics Finitary Geometry and Topology 0101 mathematics Algebra over a field Mathematics |
| Zdroj: | Linear Algebra and its Applications. 626:221-233 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2021.05.018 |
| Popis: | Let $F$ be an infinite field and let $f$ be a nonzero multilinear polynomial with coefficients in $F$. We prove that for every positive integer $d$ there exists a positive integer $s$ such that $f(M_{s}(F))$, the image of $f$ in $M_{s}(F)$, contains all trace zero $d \times d$ matrices. In particular, the image of $f$ in the algebra of all finitary matrices contains all trace zero finitary matrices. 11 pages, 0 figures, submited to Linear Algebra and Its Applications |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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