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On the factorization of non-commutative polynomials (in free associative algebras). (English) Zbl 1426.16025
Summary: We describe a simple approach to factorize non-commutative polynomials, that is, elements in free associative algebras (over a commutative field), into atoms (irreducible elements) based on (a special form of) their minimal linear representations. To be more specific, a correspondence between factorizations of an element and upper right blocks of zeros in the system matrix (of its representation) is established. The problem is then reduced to solving a system of polynomial equations (with at most quadratic terms) with commuting unknowns to compute appropriate transformation matrices (if possible).
16S36 Ordinary and skew polynomial rings and semigroup rings
68W30 Symbolic computation and algebraic computation
Full Text: DOI
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