Proof: Prime Ideal iff R/P is Integral Domain; Maximal iff R/M is Field

Описание к видео Proof: Prime Ideal iff R/P is Integral Domain; Maximal iff R/M is Field

A very useful theorem in ring theory is the theorem that an ideal P is prime if and only if the quotient R/P is an integral domain (ID). Similarly, an ideal M is maximal if and only if R/M is a field. In this video, we prove both of these statements!

Ring & Module Theory playlist:    • Ring & Module Theory  

0:00 Prime ideal
3:06 Maximal ideal
9:16 Maximal implies prime

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Music: OcularNebula - The Lopez

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