◀ ▲ ▶Branches / Algebra / Definition: Prime Ideal

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

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

Mentioned in:

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

Thank you to the contributors under CC BY-SA 4.0!

Github:

References

Adapted from CC BY-SA 3.0 Sources:

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