On splitting polynomials with noncommutative coefficients

Abstract

It is shown that for every splitting of a polynomial with noncommutative coefficients into linear factors $(X-a_k)$ with $a_k$'s commuting with coefficients, any cyclic permutation of linear factors gives the same result and all $a_k$ are roots of that polynomial. Examples are given and analyzed from Galois theory point of view.

An example analyzed in more detail, grant number corrected

References in corpus (1)

• Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs