Definition: Prime Ideal

An ideal $I\lhd R$ in a commutative ring $(R, + ,\cdot)$ is called a prime ideal, if

  1. Definition: Spectrum of a Commutative Ring
  2. Lemma: Fiber of Prime Ideals Under a Spectrum Function

Definitions: 1
Lemmas: 2 3 4
Proofs: 5 6 7
Propositions: 8

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Adapted from CC BY-SA 3.0 Sources:

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