Multilinear Polynomials Are Surjective on Algebras With Surjective Inner Derivations

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 $a_i\in A$.

arXiv comment21 pages, 0 figures, submited to Journal of Algebra

References in corpus (2)

• The images of non-commutative polynomials evaluated on $2\times 2$ matrices
• Evaluations of Noncommutative Polynomials on Algebras: Methods and Problems, and the L'vov-Kaplansky Conjecture

Cited by in corpus (4)

• Evaluations of Noncommutative Polynomials on Algebras: Methods and Problems, and the L'vov-Kaplansky Conjecture
• The Mesyan Conjecture: a restatement and a correction
• Images of Multilinear Polynomials in the Algebra of Finitary Matrices Contain Trace Zero Matrices
• The L'vov-Kaplansky Conjecture for Polynomials of Degree Three