Images of Multilinear Polynomials on Generalized Quaternion Algebras

Abstract

The main goal of this paper is to extend [J. Algebra Appl. 20 (2021), 2150074] to generalized quaternion algebras, even when these algebras are not necessarily division rings. More precisely, in such cases, the image of a multilinear polynomial evaluated on a quaternion algebra is a vector space and we additionally provide a classification of possible images.Comment: One new section is added, namely Section 3, and thus the paper is now 18 page