| Texto completo | |
| Autor(es): |
Franca, Willian
Número total de Autores: 1
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| Tipo de documento: | Artigo Científico |
| Fonte: | COMMUNICATIONS IN ALGEBRA; v. 44, n. 6, p. 2621-2634, 2016. |
| Citações Web of Science: | 3 |
| Resumo | |
Let R be a simple unital ring. Under a mild technical restriction on R, we will characterize biadditive mappings G: (RR)-R-2 satisfying G(u, u)u=uG(u, u), and G(1, r)=G(r, 1)=r for all unit uR and rR, respectively. As an application, we describe bijective linear maps : RR satisfying (xyx(-1)y(-1))=(x)(y)(x)(-1)(y)(-1) for all invertible x, yR. This solves an open problem of Herstein on multiplicative commutators. More precisely, we will show that is an isomorphism. Furthermore, we shall see the existence of a unital simple ring R without nontrivial idempotents, that admits a bijective linear map f: RR, preserving multiplicative commutators, that is not an isomorphism. (AU) | |
| Processo FAPESP: | 13/09610-6 - Identidades funcionais e um problema de Herstein |
| Beneficiário: | Willian Versolati França |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |