Multilinear Polynomials Are Surjective on Algebras With Surjective Inner Derivations

Daniel Vitas

doi:10.1016/j.jalgebra.2020.09.004

paper

Multilinear Polynomials Are Surjective on Algebras With Surjective Inner Derivations

arXiv:2106.13140 · doi:10.1016/j.jalgebra.2020.09.004

Abstract

Let $f (X_{1}, \dots, X_{n})$ be a nonzero multilinear noncommutative polynomial. If $A$ is a unital algebra with a surjective inner derivation, then every element in $A$ can be written as $f (a_{1}, \dots, a_{n})$ for some $a_{i} \in A$ .

21 pages, 0 figures, submited to Journal of Algebra