Primary decomposition of the ideal of polynomials whose fixed divisor is divisible by a prime power

Abstract

We characterize the fixed divisor of a polynomial $f(X)$ in $\mathbb{Z}[X]$ by looking at the contraction of the powers of the maximal ideals of the overring $\mathrm{Int}(\mathbb{Z})$ containing $f(X)$. Given a prime $p$ and a positive integer $n$, we also obtain a complete description of the ideal of polynomials in $\mathbb{Z}[X]$ whose fixed divisor is divisible by $p^n$ in terms of its primary components.

Fixed typos in (9) and (12)

Cited by in corpus (3)

• Properly Integral Polynomials over the Ring of Integer-valued Polynomials on a Matrix Ring
• Factorization of integer-valued polynomials with square-free denominator
• A Survey on Fixed Divisors