query: Show two $P$-primary ideals are comaximal in a Noetherian ring.
positive_passages.docid: 27766
positive_passages.text: Comaximal ideals in a commutative ring
negative_passages.docid: 41629
negative_passages.text: Structure of ideals in the product of two rings
negative_passages.docid: 97740
negative_passages.text: Homogeneous ideals are contained in homogeneous prime ideals
negative_passages.docid: 56800
negative_passages.text: Intersection of prime ideals
negative_passages.docid: 93929
negative_passages.text: The height of a principal prime ideal
negative_passages.docid: 60674
negative_passages.text: Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma
negative_passages.docid: 53801
negative_passages.text: Why are powers of coprime ideals are coprime?
negative_passages.docid: 67706
negative_passages.text: If $R$ is a Noetherian ring then $R[[x]]$ is also Noetherian
negative_passages.docid: 90889
negative_passages.text: Prime ideals in a finite direct product of rings
negative_passages.docid: 133878
negative_passages.text: Ring of order $p^2$ is commutative.
negative_passages.docid: 96071
negative_passages.text: How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
negative_passages.docid: 69710
negative_passages.text: Is it true that an ideal is primary iff its radical is prime?
negative_passages.docid: 135586
negative_passages.text: Prove that the preimage of a prime ideal is also prime.
negative_passages.docid: 50908
negative_passages.text: Showing a Ring and an Ideal are equal
negative_passages.docid: 18406
negative_passages.text: An ideal whose radical is maximal is primary
negative_passages.docid: 138882
negative_passages.text: A prime poset of ideals
negative_passages.docid: 13901
negative_passages.text: Finitely many prime ideals lying over $\mathfrak{p}$