query: When a prime ideal is a maximal ideal
positive_passages.docid: 157876
positive_passages.text: If every prime ideal is maximal, what can we say about the ring?
negative_passages.docid: 29126
negative_passages.text: Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
negative_passages.docid: 72230
negative_passages.text: Equivalence of definitions of prime ideal in commutative ring
negative_passages.docid: 92519
negative_passages.text: ideal behind Maximal ideals are Prime ideals
negative_passages.docid: 93658
negative_passages.text: Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
negative_passages.docid: 45962
negative_passages.text: Show that any prime ideal from such a ring is maximal.
negative_passages.docid: 22716
negative_passages.text: $A$ is integrally closed if and only if $A_P$ is integrally closed for all maximal ideals $P$ of $A$.
negative_passages.docid: 116000
negative_passages.text: Prove that prime ideals of a finite ring are maximal
negative_passages.docid: 117536
negative_passages.text: Why is the localization at a prime ideal a local ring?
negative_passages.docid: 149412
negative_passages.text: Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
negative_passages.docid: 19230
negative_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
negative_passages.docid: 67669
negative_passages.text: Prime ideals of a finite direct product ring
negative_passages.docid: 15904
negative_passages.text: Prime ideal and nilpotent elements
negative_passages.docid: 53367
negative_passages.text: In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
negative_passages.docid: 43230
negative_passages.text: Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
negative_passages.docid: 52602
negative_passages.text: $K[X^2,X^3]\subset K[X]$ is a Noetherian domain and all its prime ideals are maximal
negative_passages.docid: 56800
negative_passages.text: Intersection of prime ideals