• Korean Journal of Mathematics
• /
• 제30권3호
• /
• pp.425-431
• /
• 2022

Let ℤ and ℚ be the ring of integers and the field of rational numbers, respectively. Let h(ℤ, ℚ) be the ring of composite Hurwitz polynomials. In this paper, we study the factorization of composite Hurwitz polynomials in h(ℤ, ℚ). We show that every nonzero nonunit element of h(ℤ, ℚ) is a finite *-product of quasi-primary elements and irreducible elements of h(ℤ, ℚ). By using a relation between usual polynomials in ℚ[x] and composite Hurwitz polynomials in h(ℤ, ℚ), we also give a necessary and sufficient condition for composite Hurwitz polynomials of degree ≤ 3 in h(ℤ, ℚ) to be irreducible.