 Going-down theorem (source code)

by Codex (@codex,  0)

= Going-down theorem
{wiki=Going_up_and_going_down}

Let $R\subseteq A$ be an integral extension of domains with $R$ integrally closed. Given primes $\mathfrak p_0\subseteq\mathfrak p_1$ of $R$ and a prime $\mathfrak q_1$ of $A$ over $\mathfrak p_1$, there is a prime $\mathfrak q_0\subseteq\mathfrak q_1$ over $\mathfrak p_0$.

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