Polynomial in Non-Commutative Algebra

Abstract

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 $$p_1(x)=ix-xi-1$$ have no root and the polynomial $$p_k(x)=ix-xi-k$$ has the set of roots $$x=C_1+C_{2}i+\frac{1}{2}j$$ I considered division of polynomials with remainder.

English text - 24 pages; Russian text - 25 pages. Based on talk given on The Fifth Workshop New Trends in Quaternions and Octonions - NTQO 2021

References in corpus (1)

• Weierstrass method for quaternionic polynomial root-finding