| Revue: | Boletim da Sociedade Paranaense de Matematica |
| Base de datos: | PERIÓDICA |
| Número de sistema: | 000394691 |
| ISSN: | 0037-8712 |
| Autores: | Rehman, Nadeem ur1 AL-Omary, Radwan Mohammed1 Haetinger, Claus2 |
| Instituciones: | 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 |
| Año: | 2009 |
| Volumen: | 27 |
| Número: | 2 |
| Paginación: | 43-52 |
| País: | Brasil |
| Idioma: | Inglés |
| Tipo de documento: | Artículo |
| Enfoque: | Analítico |
| Resumen en inglés | Let R be a ring and α, β be automorphisms of R. An additive mapping F: R → R is called a generalized (α, β)-derivation on R if there exists an (α, β)- derivation d: R → R such that F(xy) = F(x)α(y) + β(x)d(y) holds for all x, y ∈ R. For any x, y ∈ R, set [x, y]α,β = xα(y) − β(y)x and (x ◦ y)α,β = xα(y) + β(y)x. In the present paper, we shall discuss the commutativity of a prime ring R admitting generalized (α, β)-derivations F and G satisfying any one of the following properties: (i) F([x, y]) = (x ◦ y)α,β, (ii) F(x ◦ y) = [x, y]α,β, (iii) [F(x), y]α,β = (F(x) ◦ y)α,β, (iv) F([x, y]) = [F(x), y]α,β, (v) F(x ◦ y) = (F(x) ◦ y)α,β, (vi) F([x, y] = [α(x), G(y)] and (vii) F(x ◦ y) = (α(x) ◦ G(y)) for all x, y in some appropriate subset of R. Finally, obtain some results on semi-projective Morita context with generalized (α, β)-derivations |
| Disciplinas: | Matemáticas |
| Palabras clave: | Matemáticas puras, Anillos primos, Derivaciones generalizadas, Algebra, Conmutatividad, Teoría de anillos |
| Keyword: | Mathematics, Pure mathematics, Prime rings, Generalized derivations, Algebra, Commutativity, Ring theory |
| Texte intégral: | Texto completo (Ver PDF) |
