PRIME NONASSOCIATIVE RINGS WITH SKEW DERIVATIONS
نویسندگان
چکیده
منابع مشابه
A Note on Skew Derivations in Prime Rings
Let m,n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : R −→ R be a skew derivation of R and E(x) = D(xm+n+r)−D(xm)xn+r − xmD(xn)xr − xm+nD(xr). We prove that if E(x) = 0 for all x ∈ L, then D is a usual derivation of R or R satisfies s4(x1, . . . , x4), the standard identity of degree 4.
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Let R be a commutative ring with identity. By a Bres̃ar generalized derivation of R we mean an additive map g : R→ R such that g (xy) = g (x) y + xd (y) for all x, y ∈ R, where d is a derivation of R. And an additive mapping f : R → R is called a generalized derivation in the sense of Nakajima if it satisfies f(xy) = f(x)y + xf(y) − xf(1)y for all x, y ∈ R. In this paper we extend some results o...
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ژورنال
عنوان ژورنال: Tamkang Journal of Mathematics
سال: 1997
ISSN: 2073-9826,0049-2930
DOI: 10.5556/j.tkjm.28.1997.4307