| Texto completo | |
| Autor(es): |
Kawai, Daniel
;
Ferreira, Bruno Leonardo Macedo
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. N/A, p. 14-pg., 2025-05-21. |
| Resumo | |
Given a field K and a multiplicative function M : K -> K, we classify all additive functions F and G that satisfy the functional equation F(x) + M(x)G(1/x) = 0 for all x not equal 0. A functional (form) T : U -> K is functionally homogeneous if, for some scalar function M : K -> K, T(lambda u) = M(lambda)T(u) for all lambda is an element of K, u is an element of U. A simple application of the equation in the title leads to a complete description of all biadditive forms T : V x V -> K which are functionally homogeneous. While the case Char(K)not equal 2 has been thoroughly examined by Ng [The equation f(x) + m(x)g(1/x) = 0 and homogeneous biadditive forms, Linear Algebra Appl. 93 (1987) 255-279], we focus on the remaining case where Char(K) = 2. Our results address an open problem concerning fields of characteristic 2, posed by Ferreira et al. in their recent work [B. L. M. Ferreira, A. C. Dantas and G. C. Moraes, Functional identity on division algebras, Boll. Unione Mat. Ital. 17 (2023) 667-673]. (AU) | |
| Processo FAPESP: | 22/14579-0 - Condições suficientes para isomorfismos entre isótopos de álgebras não-associativas |
| Beneficiário: | Daniel Eiti Nishida Kawai |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |