Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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IRREDUCIBLE POLYNOMIALS WITH REDUCIBLE COMPOSITIONS

  • Received : 2011.06.28
  • Accepted : 2011.07.16
  • Published : 2011.09.25
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Abstract

In this paper we investigate criteria that for an irreducible monic quadratic polynomial f(x) ${\in}$ $\mathbb{Q}$[x], $f{\circ}g$ is reducible over $\mathbb{Q}$ for an irreducible polynomial g(x) ${\in}$ $\mathbb{Q}$[x]. Odoni intrigued the discussion about an explicit form of irreducible polynomials f(x) such that $f{\cric}f$ is reducible. We construct a system of infitely many such polynomials.

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References

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