Images of Multilinear Polynomials in the Algebra of Finitary Matrices Contain Trace Zero Matrices
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2021
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916518779944960 |
|---|---|
| author | Vitas, Daniel |
| author_facet | Vitas, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_00539 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Images of Multilinear Polynomials in the Algebra of Finitary Matrices Contain Trace Zero Matrices Vitas, Daniel Rings and Algebras 16R99, 16W25 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. |
| title | Images of Multilinear Polynomials in the Algebra of Finitary Matrices Contain Trace Zero Matrices |
| topic | Rings and Algebras 16R99, 16W25 |
| url | https://arxiv.org/abs/2108.00539 |