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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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Adapted from CC BY-SA 3.0 Sources:
- Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück