Algebraic Number Theory
《Algebraic Number Theory》 · 第 22 页 · Chapter I，Section 3「Ideals」，Corollary 3.9
Every fractional ideal $\mathfrak a$ admits a unique representation as a product $\mathfrak a=\prod_{\mathfrak p}\mathfrak p^{v_{\mathfrak p}}$ with $v_{\mathfrak p}\in\mathbb Z$ and $v_{\mathfrak p}=0$ for almost all $\mathfrak p$. […] Every fractional ideal $\mathfrak a$ is a quotient of two integral ideals, which by (3.3) have a prime decomposition. Therefore $\mathfrak a$ has a prime decomposition of the type stated in the corollary.