Polynomial in Non-Commutative Algebra

2021/11/30 by Aleks Kleyn, Kleyn, Aleks
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #General Mathematics (math.GM) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2112.00613

openalex publication_date 2021/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 p₁(x)=ix-xi-1 have no root and the polynomial p_k(x)=ix-xi-k has the set of roots x=C₁+C₂i+\frac 12 j I considered division of polynomials with remainder.

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