Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs

Abstract

To directed graphs with unique sink and source we associate a noncommutative associative alsgebra and a polynomial over this algebra. Edges of the graph correspond to pseudo-roots of the polynomial. We give a sufficient condition when coefficients of the polynomial can be rationally expressed via elements of a given set of pseudo-roots (edges). Our results are based on a new theorem for directed graphs also proved in this paper.

15 pages, AMSTeX

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