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On Ritt's Factorization of Polynomials
Author(s) -
Beardon A. F.,
Ng T. W.
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001046
Subject(s) - mathematics , factorization , invariant (physics) , polynomial , factorization of polynomials , pure mathematics , set (abstract data type) , composition (language) , decomposition , algebra over a field , discrete mathematics , computer science , mathematical analysis , algorithm , matrix polynomial , linguistics , philosophy , mathematical physics , programming language , ecology , biology
Ritt has shown that any complex polynomial p can be written as the composition of polynomials p 1 ,…, p m , where each p j is prime in the sense that it cannot be written as a non‐trivial composition of polynomials. The factors p j are not unique but the number m of them is, as is the set of the degrees of the p j . The paper extends Ritt's theory and, in particular, a third invariant of the decomposition is introduced.