Definition: Prime Ideal
An ideal $I\lhd R$ in a commutative ring $(R, + ,\cdot)$ is called a prime ideal, if
 $I\neq R$ and
 for any $r,s\in R$ with $rs\in I$ it follows $r\in I$ or $s\in I.$
Table of Contents
 Definition: Spectrum of a Commutative Ring
 Lemma: Fiber of Prime Ideals Under a Spectrum Function
Mentioned in:
Definitions: 1
Lemmas: 2 3 4
Proofs: 5 6 7
Propositions: 8
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References
Adapted from CC BYSA 3.0 Sources:
 Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück