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Vanishing Derivations on Some Subsets in Prime Rings Involving Generalized Derivations
Bulletin of the Malaysian Mathematical Sciences Society ( IF 1.2 ) Pub Date : 2021-02-12 , DOI: 10.1007/s40840-021-01080-4 Basudeb Dhara , Vincenzo De Filippis , Manami Bera
中文翻译:
涉及广义导数的素环中某些子集的消失导数
更新日期:2021-02-12
Bulletin of the Malaysian Mathematical Sciences Society ( IF 1.2 ) Pub Date : 2021-02-12 , DOI: 10.1007/s40840-021-01080-4 Basudeb Dhara , Vincenzo De Filippis , Manami Bera
Let R be a noncommutative prime ring of characteristic different from 2 and 3, C the extended centroid of R, F and G two generalized derivations of R, d a nonzero derivation of R and \(f(x_1,\ldots ,x_n)\) a multilinear polynomial over C. Suppose that I is a nonzero ideal of R and \(f(I)=\{f(x_1,\ldots ,x_n)| x_1,\ldots ,x_n\in I\}\). If \(f(x_1,\ldots ,x_n)\) is not central valued on R and
$$\begin{aligned} d(F^2(u)u-G(u^2))=0 \end{aligned}$$for all \(u\in f(I)\), then all possible forms of the maps F, G and d are described in the present paper.
中文翻译:
涉及广义导数的素环中某些子集的消失导数
让- [R是从图2和3的特性不同的非交换素环,Ç的扩展形心- [R ,˚F和G ^ 2广义的推导- [R ,d非零的推导ř和\(F(X_1,\ ldots,x_n)\ )C上的多元多项式。假设我是R和\(f(I)= \ {f(x_1,\ ldots,x_n)| x_1,\ ldots,x_n \ in I \} \)的非零理想。如果\(F(X_1,\ ldots,x_n)\)不是中央值上- [R和
$$ \ begin {aligned} d(F ^ 2(u)uG(u ^ 2))= 0 \ end {aligned} $$对于所有\(u \ in f(I)\),然后在本文中描述映射F,G和d的所有可能形式。