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Lemma: Fiber of Maximal Ideals

Let \(R\) and \(S\) be commutative rings and let \(\varphi :R\rightarrow S\) be a ring homomorphism. Further, let \(I\subseteq S\) be a maximal ideal in \(S\). Then the fiber \(\varphi ^{-1}(I)\subseteq R\) is not necessarily a maximal ideal.

Table of Contents

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