Commutators with idempotent values on multilinear polynomials in prime rings

Proceedings Mathematical Sciences

关键词: Multilinear polynomial;    derivations;    generalized polynomial identity;    prime ring;    right ideal.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let $R$ be a prime ring of characteristic different from 2, $C$ its extended centroid, $d$ a nonzero derivation of $R$, $f (x_1,ldots , x_n)$ a multilinear polynomial over $C$, $varrho$ a nonzero right ideal of $R$ and $m > 1$ a fixed integer such that $$([d(f (r_1, ldots , r_n)), f (r_1, ldots , _n)])^m = [d(f (r_1, ldots , r_n)), f(r_1, ldots , r_n)]$$ for all $r_1, ldots , r_n invarrho$. Then either $[f(x_1, ldots , x_n), x_{n+1}]x_{n+2}$ is an identity for $varrho$ or $d(varrho)varrho = 0$.

【 授权许可】

Unknown