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On splitting polynomials with noncommutative coefficients
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math.QAmath.RA
keywords
coefficientsfactorslinearnoncommutativepolynomialsplittinganalyzedcommuting
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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.
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