On Jordan ideals and left(θ,θ)-derivations in prime rings
2004 ◽
Vol 2004
(37)
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pp. 1957-1964
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LetRbe a ring andSa nonempty subset ofR. Suppose thatθandϕare endomorphisms ofR. An additive mappingδ:R→Ris called a left(θ,ϕ)-derivation (resp., Jordan left(θ,ϕ)-derivation) onSifδ(xy)=θ(x)δ(y)+ϕ(y)δ(x)(resp.,δ(x2)=θ(x)δ(x)+ϕ(x)δ(x)) holds for allx,y∈S. Suppose thatJis a Jordan ideal and a subring of a2-torsion-free prime ringR. In the present paper, it is shown that ifθis an automorphism ofRsuch thatδ(x2)=2θ(x)δ(x)holds for allx∈J, then eitherJ⫅Z(R)orδ(J)=(0). Further, a study of left(θ,θ)-derivations of a prime ringRhas been made which acts either as a homomorphism or as an antihomomorphism of the ringR.
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2012 ◽
Vol 31
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pp. 65-70
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2014 ◽
Vol 33
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Vol 39
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pp. 249-255
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1982 ◽
Vol 32
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Vol 23
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