English

On the rational relationships among pseudo-roots of a non-commutative polynomial

Rings and Algebras 2020-08-28 v3 Combinatorics

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.

Keywords

Cite

@article{arxiv.2001.04856,
  title  = {On the rational relationships among pseudo-roots of a non-commutative polynomial},
  author = {Vladimir Retakh and Michael Saks},
  journal= {arXiv preprint arXiv:2001.04856},
  year   = {2020}
}

Comments

Minor corrections, to appear in "Journal of Pure and Applied Algebra"