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Lemma: Prime Ideals of Multiplicative Systems in Integral Domains

Let $R$ be an integral domain and let $S\subseteq R$ be its multiplicative system. If $I$ is a prime ideal of $R_S$, then it is also a prime ideal of $R$ such that $S\cap I=\emptyset$.

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Proofs: 1

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References

Adapted from CC BY-SA 3.0 Sources:

1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück