On splitting polynomials with noncommutative coefficients
Abstract
Description
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
An example analyzed in more detail, grant number corrected