query: Non-principal prime ideals of $\mathbb{Z}[x]$
positive_passages.docid: 37929
positive_passages.text: Classification of prime ideals of $\mathbb{Z}[X]$
negative_passages.docid: 141687
negative_passages.text: Nonprincipal prime ideals contain two relatively prime elements
negative_passages.docid: 44083
negative_passages.text: prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
negative_passages.docid: 128813
negative_passages.text: Examples of a commutative ring without an identity in which a maximal ideal is not a prime ideal
negative_passages.docid: 138882
negative_passages.text: A prime poset of ideals
negative_passages.docid: 31585
negative_passages.text: Primary ideals of $\mathbb{Z}$
negative_passages.docid: 109691
negative_passages.text: When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
negative_passages.docid: 110984
negative_passages.text: Ideals and prime ideals in a commutative ring.
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: 33576
negative_passages.text: Non-principal ideal in $K[x,y]$?
negative_passages.docid: 149747
negative_passages.text: Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
negative_passages.docid: 87101
negative_passages.text: Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
negative_passages.docid: 97740
negative_passages.text: Homogeneous ideals are contained in homogeneous prime ideals
negative_passages.docid: 133975
negative_passages.text: Localising a polynomial ring and non-maximal prime ideal
negative_passages.docid: 3037
negative_passages.text: Integral domain without unity has prime characteristic?
negative_passages.docid: 1720
negative_passages.text: Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
negative_passages.docid: 85915
negative_passages.text: Principal prime ideals are minimal among prime ideals in a UFD