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

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

2005-09-12

arxiv.org/abs/math/0509260v1

Mathematics

Quantum Algebra

15 pages, AMSTeX

Scientific paper

10.1007/s11005-005-0024-8

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.

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