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Let $R$ be a prime ring of characteristic different from $2$. Suppose that $F$, $G$, $H$ and $T$ are generalized derivations of $R$. Let $U$ be the Utumi quotient ring of $R$ and $C$ be the center of $U$, called the extended centroid of $R$ and let $f(x_1,\ldots,x_n)$ be a non central multilinear polynomial over $C$. If \begin{align*} &\ F(f(r_1,\ldots,r_n))G(f(r_1,\ldots,r_n))-f(r_1,\ldots,r_n)T(f(r_1,\ldots,r_n))\\ =&\ H(f(r_1,\ldots,r_n)^2) \end{align*} for all $r_1, \ldots, r_n \in R$, then we describe all possible forms of $F$, $G$, $H$ and $T$.
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참고문헌 (30)
참고문헌 신청
Nurcan Argaç / 2012 / Actions of Generalized Derivations on Multilinear Polynomials in Prime Rings / Algebra Colloquium 18(spec01):955~964
A. Asma / 2003 / On Lie ideals with derivations as homomorphisms and anti-homomorphisms / Acta Mathematica Hungarica 101(1/2):79~82
K. I. Beidar / 1996 / Rings with generalized identities / Marcel Dekker, Inc
H. E. Bell / 1989 / Rings in which derivations satisfy certain algebraic conditions / Acta Mathematica Hungarica 53(3-4):339~346
Matej Bresar / 1991 / On the distance of the composition of two derivations to the generalized derivations / Glasgow Mathematical Journal 33(1):89~93
A. Asma / 2003 / On Lie ideals with derivations as homomorphisms and anti-homomorphisms / Acta Mathematica Hungarica 101(1/2):79~82
K. I. Beidar / 1996 / Rings with generalized identities / Marcel Dekker, Inc
H. E. Bell / 1989 / Rings in which derivations satisfy certain algebraic conditions / Acta Mathematica Hungarica 53(3-4):339~346
Matej Bresar / 1991 / On the distance of the composition of two derivations to the generalized derivations / Glasgow Mathematical Journal 33(1):89~93
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