### Abstract

In order to fully understand the factorization behavior of the ring Int(ℤ) = {f ∈ ℚ[x] | f (ℤ) ⊆ ℤ} of integer-valued polynomials on ℤ, it is crucial to identify the irreducible elements. Peruginelli [8] gives an algorithmic criterion to recognize whether an integer-valued polynomial g/d is irreducible in the case where d is a square-free integer and g ∈ ℤ[x] has fixed divisor d. For integer-valued polynomials with arbitrary composite denominators, so far there is no algorithmic criterion known to recognize whether they are irreducible. We describe a computational method which allows us to recognize all irreducible polynomials in Int(ℤ). We present some known facts, preliminary new results and open questions.

Original language | English |
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Title of host publication | ITM Web of Conferences |

Number of pages | 10 |

Volume | 20 |

DOIs | |

Publication status | Published - 12 Oct 2018 |

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## Cite this

Nakato, S., Rissner, R., & Antoniou, A. (2018). Irreducible polynomials in Int(Z). In

*ITM Web of Conferences*(Vol. 20). [01004] https://doi.org/10.1051/itmconf/20182001004