A <modulus of a number field> is a formal product
$$
\mathfrak m=\mathfrak m_0\mathfrak m_\infty,
$$
where $\mathfrak m_0=\prod_{\mathfrak p}\mathfrak p^{n_\mathfrak p}$ is a nonzero integral ideal and $\mathfrak m_\infty$ is a product of distinct real embeddings of $K$. Only finitely many $n_\mathfrak p$ are nonzero; complex places do not occur.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 123 / 1 / a / Solution

{wiki=Modulus_(algebraic_number_theory)}

A modulus is a formal product $\mathfrak m=\mathfrak m_0\mathfrak m_\infty$, where $\mathfrak m_0$ is a nonzero integral ideal and $\mathfrak m_\infty$ is a product of distinct real places.


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