| Full text | |
| Author(s): |
Franca, Willian
Total Authors: 1
|
| Document type: | Journal article |
| Source: | COMMUNICATIONS IN ALGEBRA; v. 44, n. 6, p. 2621-2634, 2016. |
| Web of Science Citations: | 3 |
| Abstract | |
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) | |
| FAPESP's process: | 13/09610-6 - Functional identities and Herstein's problem |
| Grantee: | Willian Versolati França |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |