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

Vladimir Retakh; Michael Saks

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arXiv · 2001.04856

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

Vladimir Retakh·Michael Saks

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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.

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Vladimir Retakh, Michael Saks. 2020-01-14. On the rational relationships among pseudo-roots of a non-commutative polynomial. https://arxiv.org/abs/2001.04856

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