@techreport{460226f7573f48de95cdf4431d0437b0,

title = "On the Factorization of Non-Commutative Polynomials (in Free Associative Algebras)",

abstract = "We describe a simple approach to factorize non-commutative (nc) 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).",

keywords = "math.RA, Primary 16K40, 16Z05, Secondary 16G99, 16S10, math.RA, 16K40, 16Z05 (Primary), 16G99, 16S10 (Secondary)",

author = "Konrad Schrempf",

note = "22 pages",

year = "2017",

month = jun,

day = "6",

language = "English",

series = "arXiv.org e-Print archive",

publisher = "Cornell University Library",

pages = "1--22",

type = "WorkingPaper",

institution = "Cornell University Library",

}