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IRREDUCIBLE POLYNOMIALS WITH REDUCIBLE COMPOSITIONS
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  • Journal title : Honam Mathematical Journal
  • Volume 33, Issue 3,  2011, pp.355-366
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2011.33.3.355
 Title & Authors
IRREDUCIBLE POLYNOMIALS WITH REDUCIBLE COMPOSITIONS
Choi, Eun-Mi;
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 Abstract
In this paper we investigate criteria that for an irreducible monic quadratic polynomial f(x) [x], is reducible over for an irreducible polynomial g(x) [x]. Odoni intrigued the discussion about an explicit form of irreducible polynomials f(x) such that is reducible. We construct a system of infitely many such polynomials.
 Keywords
Resultant;Discriminant;Iterated polynomial;
 Language
English
 Cited by
 References
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N. Ali, On the irreducibility for composition of polynomials. International Mathematical Forum, 4, (40), 2009, 2001-2008

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L. Danielson, B. Fein. On the irreducibility of iterates of $x^n-b$, The Americal Math. Soc. 130 (2011), 1589-1596.

3.
R.K.W. Odoni. The Galois theory of iterates and composites of polynomials, Prod. London Math Soc. (3), 51 (3), 1985, 385-414 crossref(new window)

4.
R.K.W. Odoni. On the prime divisors of the sequence $w_{n+1}=1+w_1{\cdot}{\cdot}{\cdot}w_n.$ J. London Math. Soc. 32 (1985), 1-11. crossref(new window)