We characterize the fixed divisor of a polynomial $f(X)$ in $\Z[X]$ by looking at the contraction of the powers of the maximal ideals of the overring $\IZ$ containing $f(X)$. Given a prime $p$ and a positive integer $n$, we also obtain a complete description of the ideal of polynomials in $\Z[X]$ whose fixed divisor is divisible by $p^n$ in terms of its primary components.
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机译：我们通过查看包含$ f（X）$的压倒性$ \ IZ $的最大理想幂的压缩来刻画$ \ Z [X] $中多项式$ f（X）$的固定除数。给定一个质数$ p $和一个正整数$ n $，我们还可以获得$ \ Z [X] $中多项式的理想项的完整描述，其固定除数可以被其主要成分除以$ p ^ n $ 。
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