Polynomial in Non-Commutative Algebra скачать в хорошем качестве

Polynomial in Non-Commutative Algebra

I considered definition and properties of polynomial in no-commutative algebra. There exists polynomial which has finite, infinite or empty set of roots. For instance, the polynomial p1(x)=ix-xi-1 have no root and the polynomial pk(x)=ix-xi-k has the set of roots x=C1+C2i+1/2 j I considered division of polynomials with remainder. My point of view on polynomials in non-commutative algebra is different from the generally accepted. Despite the fact that considering of right-sided polynomial or left-sided polynomial simplifies theory of polynomials, this leads to errors in particular calculations. In my speech, I considered the set of polynomials with given roots and algorithm of division of polynomials. Numerous examples show that factorization of the polynomial is polylinear map of factors. But the details are yet to be explored.