query: Finite quotient ring over prime ideals
positive_passages.docid: 19230
positive_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
negative_passages.docid: 19883
negative_passages.text: Prime ideals of the matrix ring
negative_passages.docid: 148434
negative_passages.text: Ring where irreducibles are primes which is not an UFD
negative_passages.docid: 94157
negative_passages.text: Normal Ring and Prime Ideal whose Square is Principal
negative_passages.docid: 15904
negative_passages.text: Prime ideal and nilpotent elements
negative_passages.docid: 94174
negative_passages.text: Ring of polynomials over a field has infinitely many primes
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: 93629
negative_passages.text: Ideal quotient of fractional ideals
negative_passages.docid: 98818
negative_passages.text: Quotient ring of a localization of a ring
negative_passages.docid: 37929
negative_passages.text: Classification of prime ideals of $\mathbb{Z}[X]$
negative_passages.docid: 62917
negative_passages.text: Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
negative_passages.docid: 53770
negative_passages.text: Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
negative_passages.docid: 130466
negative_passages.text: Proving every prime ideal is maximal in a finite dimensional ring over a field.
negative_passages.docid: 111114
negative_passages.text: Prove that an ideal in $k[x,y]$ is a prime ideal
negative_passages.docid: 129302
negative_passages.text: Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
negative_passages.docid: 138882
negative_passages.text: A prime poset of ideals
negative_passages.docid: 28518
negative_passages.text: Hom of finitely generated modules over a noetherian ring