On Lie Structure of Prime Rings with Generalized (α, β)-Derivations



Título del documento: On Lie Structure of Prime Rings with Generalized (α, β)-Derivations
Revista: Boletim da Sociedade Paranaense de Matematica
Base de datos: PERIÓDICA
Número de sistema: 000394691
ISSN: 0037-8712
Autores: 1
1
2
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:
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
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