TY - GEN

T1 - Irreducible polynomials in Int(Z).

AU - Nakato, Sarah

AU - Rissner, Roswitha

AU - Antoniou, Austin

PY - 2018/10/12

Y1 - 2018/10/12

N2 - 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.

AB - 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.

UR - https://creativecommons.org/licenses/by/4.0/

U2 - 10.1051/itmconf/20182001004

DO - 10.1051/itmconf/20182001004

M3 - Conference contribution

VL - 20

BT - ITM Web of Conferences

ER -