| Journal: | Boletim da Sociedade Paranaense de Matematica |
| Database: | PERIÓDICA |
| System number: | 000395377 |
| ISSN: | 0037-8712 |
| Authors: | Ali, Shakir1 Haetinger, Claus2 |
| Institutions: | 1Aligarh Muslim University, Department of Mathematics, Aligarh, Uttar Pradesh. India 2Centro Universitario UNIVATES, Centro de Ciencias Exatas e Tecnologicas, Lajeado, Rio Grande do Sul. Brasil |
| Year: | 2008 |
| Volumen: | 26 |
| Number: | 1-2 |
| Pages: | 71–80-71–80 |
| Country: | Brasil |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Analítico |
| English abstract | Let R be a ring, and α be an endomorphism of R. An additive mapping H: R → R is called a left α-centralizer (resp. Jordan left α-centralizer) if H(xy) = H(x)α(y) for all x, y ∈ R (resp. H(x 2 ) = H(x)α(x) for all x ∈ R). The purpose of this paper is to prove two results concerning Jordan α-centralizers and one result related to generalized Jordan (α, β)-derivations. The result which we refer state as follows: Let R be a 2-torsion-free semiprime ring, and α be an automorphism of R. If H: R → R is an additive mapping such that H(x 2 ) = H(x)α(x) for every x ∈ R or H(xyx) = H(x)α(yx) for all x, y ∈ R, then H is a left α-centralizer on R. Secondly, this result is used to prove that every generalized Jordan (α, β)-derivation on a 2-torsion-free semiprime ring is a generalized (α, β)-derivation. Finally, some examples are given to demonstrate that the restrictions imposed on the hypothesis of the various theorems were not superfluous |
| Disciplines: | Matemáticas |
| Keyword: | Matemáticas puras, Algebra, Teoría de anillos, Anillos primos, Algebras de Lie, Centralizadores, Derivación, Algebras de Jordan |
| Keyword: | Mathematics, Pure mathematics, Algebra, Ring theory, Prime rings, Lie algebras, Centralizers, Derivation, Jordan algebras |
| Full text: | Texto completo (Ver PDF) |
