query: Non-maximal prime ideal that is maximal among prime ideals
positive_passages.docid: 28629
positive_passages.text: Is the axiom of choice necessary to prove that closed points in the Zariski topology are maximal ideals?
negative_passages.docid: 134991
negative_passages.text: Commutative non Noetherian rings in which all maximal ideals are finitely generated
negative_passages.docid: 133975
negative_passages.text: Localising a polynomial ring and non-maximal prime ideal
negative_passages.docid: 48273
negative_passages.text: If a maximal subgroup is normal, it has prime index
negative_passages.docid: 43230
negative_passages.text: Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
negative_passages.docid: 154239
negative_passages.text: Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
negative_passages.docid: 30714
negative_passages.text: A question on ring homomorphisms and maximal ideals.
negative_passages.docid: 151829
negative_passages.text: Why are maximal ideals prime?
negative_passages.docid: 90314
negative_passages.text: Maximal ideals in $R[x]$
negative_passages.docid: 37929
negative_passages.text: Classification of prime ideals of $\mathbb{Z}[X]$
negative_passages.docid: 147871
negative_passages.text: How do the prime ideals of $\mathbb{Z}_{k}$ look like?
negative_passages.docid: 148434
negative_passages.text: Ring where irreducibles are primes which is not an UFD
negative_passages.docid: 42170
negative_passages.text: $R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
negative_passages.docid: 116000
negative_passages.text: Prove that prime ideals of a finite ring are maximal
negative_passages.docid: 104486
negative_passages.text: Ideal in $\mathbb Z[x]$ which is not two-generated
negative_passages.docid: 130466
negative_passages.text: Proving every prime ideal is maximal in a finite dimensional ring over a field.
negative_passages.docid: 92585
negative_passages.text: If krull dimension is $0$, then all prime ideals are maximal?