Jordan α-centralizers in rings and some applications



Título del documento: Jordan α-centralizers in rings and some applications
Revista: Boletim da Sociedade Paranaense de Matematica
Base de datos: PERIÓDICA
Número de sistema: 000395377
ISSN: 0037-8712
Autores: 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: 26
Número: 1-2
Paginación: 71–80-71–80
País: Brasil
Idioma: Inglés
Tipo de documento: Artículo
Enfoque: Analítico
Resumen en inglés 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
Disciplinas: Matemáticas
Palabras clave: 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
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