2015/05/13 by Vladimir Bolotnikov, Bolotnikov, Vladimir
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.1505.03573
arxiv created 2015/05/13 · openalex publication_date 2015/05/13 · arxiv updated 2015/05/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
It is known that polynomials over quaternions may have spherical zeros and isolated left and right zeros. These zeros along with appropriately defined multiplicities form the zero structure of a polynomial. In this paper, we equivalently describe the zero structure of a polynomial in terms of its left and right spherical divisors as well as in terms of left and right indecomposable divisors. Several algorithms are proposed to find left/right zeros and left/right spherical divisors of a quaternion polynomial, to construct a polynomial with prescribed zero structure and more generally, to construct the least left/right common multiple of given polynomials. Similar questions are briefly discussed in the setting of quaternion formal power series.