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https://www.ias.ac.in/article/fulltext/pmsc/127/01/0091-0098

Multilinear polynomial; derivations; generalized polynomial identity; prime ring; right ideal.

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 $r_1, \ldots , r_n \in\varrho$. Then either $[f(x_1, \ldots , x_n), x_{n+1}]x_{n+2}$ is an identity for $\varrho$ or $d(\varrho)\varrho = 0$.

Published

1 February 2017

Manuscript received

15 June 2015

Manuscript revised

5 January 2016

Accepted

26 July 2015