----- > [!proposition] Proposition. ([[existence of maximal ideals in commutative rings]]) > Let $I \neq \langle 1 \rangle$ be a proper [[ideal]] of a [[commutative ring|commutative]] [[ring]] $R$. Then there exists a [[maximal ideal]] $\mathfrak{m}$ of $R$ containing $I$. ^proposition > [!proof]- Proof. ([[existence of maximal ideals in commutative rings]]) > Application of [[Zorn's lemma]]. ----- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```