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2 results on '"16K99 (Primary) 06C99 (Secondary)"'

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

Author

Retakh, Vladimir and Saks, Michael

Subjects
Mathematics - Rings and Algebras, Mathematics - Combinatorics, 16K99 (Primary) 06C99 (Secondary)
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., Comment: Minor corrections, to appear in "Journal of Pure and Applied Algebra"

Published
2020

2. 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

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