1. On the rational relationships among pseudo-roots of a non-commutative polynomial
- Author
-
Vladimir Retakh and Michael Saks
- Subjects
Polynomial ,Algebra and Number Theory ,Graph theoretic ,010102 general mathematics ,Mathematics - Rings and Algebras ,01 natural sciences ,Combinatorics ,Rings and Algebras (math.RA) ,Lattice (order) ,0103 physical sciences ,FOS: Mathematics ,Division ring ,Greatest common divisor ,Mathematics - Combinatorics ,16K99 (Primary) 06C99 (Secondary) ,Combinatorics (math.CO) ,010307 mathematical physics ,0101 mathematics ,Commutative property ,Monic polynomial ,Least common multiple ,Mathematics - Abstract
For a non-commutative ring R, we consider factorizations of polynomials in R[t] where t is a central variable. A pseudo-root of a polynomial p(t) is an element x in R, for which there exist polynomials q(t) and s(t) such that p(t)=q(t)(t-x)s(t). We investigate the rational relationships that hold among the pseudo-roots of p(t) by using the diamond operations for cover graphs of modular lattices., Minor corrections, to appear in "Journal of Pure and Applied Algebra"
- Published
- 2021