Notes on (α,β)-derivations
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′...
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| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297001105 |
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| _version_ | 1832558159074426880 |
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| author | Neşet Aydin |
| author_facet | Neşet Aydin |
| author_sort | Neşet Aydin |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-252cc6211b5b4d999c78cd8cd76560d6 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-252cc6211b5b4d999c78cd8cd76560d62025-02-03T01:33:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120481381610.1155/S0161171297001105Notes on (α,β)-derivationsNeşet Aydin0Adnan Menderes University, Faculty of Arts and Sciences, Department of Mathematics, Aydin 0910, TurkeyLet 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.http://dx.doi.org/10.1155/S0161171297001105derivationsemiprime ringprime ringcommutative. |
| spellingShingle | Neşet Aydin Notes on (α,β)-derivations International Journal of Mathematics and Mathematical Sciences derivation semiprime ring prime ring commutative. |
| title | Notes on (α,β)-derivations |
| title_full | Notes on (α,β)-derivations |
| title_fullStr | Notes on (α,β)-derivations |
| title_full_unstemmed | Notes on (α,β)-derivations |
| title_short | Notes on (α,β)-derivations |
| title_sort | notes on α β derivations |
| topic | derivation semiprime ring prime ring commutative. |
| url | http://dx.doi.org/10.1155/S0161171297001105 |
| work_keys_str_mv | AT nesetaydin notesonabderivations |