LIE IDEALS AND DERIVATIONS OF σ-PRIME RINGS
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초록
Let R be a 2-torsion free σ-prime ring with an involution σ, U a nonzero square closed σ-Lie ideal, Z(R) the center of R and d a derivation of R. In this paper, it is proved that d = 0 or U ⊆ Z(R) if one of the following conditions holds:(1) d(xy)-xy ∈ Z(R) or d(xy)-yx ∈ Z(R) for all x,y ∈ U. (2) d(x)?d(y) = 0 or d(x)?d(y) = xｏy forall x,y ∈ U and d commutes with σ.
Abstract
Let R be a 2-torsion free σ-prime ring with an involution σ, U a nonzero square closed σ-Lie ideal, Z(R) the center of R and d a derivation of R. In this paper, it is proved that d = 0 or U ⊆ Z(R) if one of the following conditions holds:(1) d(xy)-xy ∈ Z(R) or d(xy)-yx ∈ Z(R) for all x,y ∈ U. (2) d(x)?d(y) = 0 or d(x)?d(y) = xｏy forall x,y ∈ U and d commutes with σ.
참고문헌 (12)
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