Notes on (α,β)-derivations
| Autor: | Neşet Aydin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 1997 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 20, Iss 4, Pp 813-816 (1997) |
| Druh dokumentu: | article |
| ISSN: | 0161-1712 1687-0425 01611712 |
| DOI: | 10.1155/S0161171297001105 |
| Popis: | Let R be a prime ring of characteristic not 2, U a nonzero ideal of R and 0≠da(α,β)-derivation of R where α and β are automorphisms of R. i) [d(U),a]=0 then a∈Z ii) For a,b∈R, the following conditions are equivalent (I) α(a)d(x)=d(x)β(b), for all x∈U (II) Either α(a)=β(b)∈CR(d(U)) or CR(a)=CR(b)=R′ and a[a,x]=[a,x]b (or a[b,x]=[b,x]b) for all x∈U. Let R be a 2-torsion free semiprime ring and U be a nonzero ideal of R iii) Let d be a (α,β)-derivation of R and g be a (γ,δ)-derivation of R. Suppose that dg is a (αγ,βδ)-derivation and g commutes both γ and δ then g(x)Uα−1d(y)=0, for all x,y∈U iv) Let Ann(U)=0 and d be an (α,β)-derivation of Rand g be a (λ,δ)-derivation of R such that g commutes both γ, and δ. If for all x,y∈U, β−1(d(x))Ug(y)=0=g(x)Uα−1(d(y)) then dg is a (αγ,βδ)-derivation on R. |
| Databáze: | Directory of Open Access Journals |
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