| Texto completo | |
| Autor(es): |
Bajuk, Zan
;
Bresar, Matej
;
Fagundes, Pedro
;
Ioppolo, Antonio
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Algebra; v. 647, p. 35-pg., 2024-03-14. |
| Resumo | |
Let f = f (x (1) , . . . , x (m) ) be a multilinear polynomial over a field F. An F-algebra A is said to be f-zpd (f -zero product determined) if every m-linear functional phi: A (m) -> F which preserves zeros of f is of the form phi(a (1) , . . . , a (m) ) = tau (f (a (1) , . . . , a (m) )) for some linear functional tau on A. We are primarily interested in the question whether the matrix algebra M (d) (F) is f-zpd. While the answer is negative in general, we provide several families of polynomials for which it is positive. We also consider a related problem on the form of a multilinear polynomial g = g(x (1) , ... , x (m) ) with the property that every zero of f in M (d) (F)( m) is a zero of g. Under the assumption that m < 2d -3, we show that g and f are linearly dependent. (c) 2024 Elsevier Inc. All rights reserved. (AU) | |
| Processo FAPESP: | 22/05256-2 - Imagens de polinômios multilineares sobre UT_2 e UT_3 com involuções |
| Beneficiário: | Pedro Souza Fagundes |
| Modalidade de apoio: | Bolsas no Exterior - Estágio de Pesquisa - Doutorado |
| Processo FAPESP: | 19/16994-1 - Álgebras que são soma de duas subálgebras PI |
| Beneficiário: | Pedro Souza Fagundes |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |