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A Note on Multiplicative (Generalized) (α, β)-Derivations in Prime Rings
- Source :
- Annales Mathematicae Silesianae, Vol 33, Iss 1, Pp 266-275 (2019)
- Publication Year :
- 2019
- Publisher :
- Sciendo, 2019.
-
Abstract
- Let R be a prime ring with center Z(R). A map G : R →R is called a multiplicative (generalized) (α, β)-derivation if G(xy)= G(x)α(y)+β(x)g(y) is fulfilled for all x; y ∈ R, where g : R → R is any map (not necessarily derivation) and α; β : R → R are automorphisms. Suppose that G and H are two multiplicative (generalized) (α, β)-derivations associated with the mappings g and h, respectively, on R and α, β are automorphisms of R. The main objective of the present paper is to investigate the following algebraic identities: (i) G(xy) + α(xy) = 0, (ii) G(xy) + α(yx) = 0, (iii) G(xy) + G(x)G(y) = 0, (iv) G(xy) = α(y) ○ H(x) and (v) G(xy) = [α(y), H(x)] for all x, y in an appropriate subset of R.
Details
- Language :
- English
- ISSN :
- 23914238
- Volume :
- 33
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Annales Mathematicae Silesianae
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.33097ba091614138acb1bb01a2d74cf8
- Document Type :
- article
- Full Text :
- https://doi.org/10.2478/amsil-2019-0008