Derivations With Invertible Values on a Multilinear Polynomial
Derivations With Invertible Values on a Multilinear Polynomial
Let $R$ be a semiprime $K$-algebra with unity, $d$ a nonzero derivation of $R$, and $f({x_1}, \ldots ,{x_t})$ a monic multilinear polynomial over $K$ such that $d(f({a_1}, \ldots ,{a_t})) \ne 0$ for some ${a_1}, \ldots ,{a_t} \in R$. It is shown that if for every ${r_1}, \ldots ,{r_t}$ in $R$ …