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- Title
ONE-SIDED GENERALIZED (α, β)--REVERSE DERIVATIONS OF ASSOCIATIVE RINGS.
- Authors
Engin, Ayşe; Aydın, Neşet
- Abstract
In this paper, we introduce the notion of the one-sided generalized (α, β)-reverse derivation of a ring R. Let R be a semiprime ring, ϱ be a non-zero ideal of R, α be an epimorphism of ϱ, β be a homomorphism of ϱ (α be a homomorphism of ϱ, β be an epimorphism of ϱ) and γ: ϱ → R be a non-zero (α, β)-reverse derivation. We show that there exists F: ϱ → R, an l-generalized (α, β)-reverse derivation (an r-generalized (α, β)-reverse derivation) associated with γ iff F(ϱ), γ(ϱ) ⊂ CR(ϱ) and F is an r-generalized (β, α)-derivation (an l-generalized (β, α)-derivation) associated with (β, α)-derivation γ on ϱ. This theorem generalized the results of A. Aboubakr and S. Gonzalez proved in [1, Theorem 3.1 and Theorem 3.2 ].
- Subjects
ASSOCIATIVE rings; HOMOMORPHISMS; MORPHISMS (Mathematics)
- Publication
Facta Universitatis, Series: Mathematics & Informatics, 2024, Vol 39, Issue 1, p21
- ISSN
0352-9665
- Publication type
Article
- DOI
10.22190/FUMI220322001E