query: a question on complement of prime ideal
positive_passages.docid: 120149
positive_passages.text: Is the complement of a prime ideal closed under both addition and multiplication?
negative_passages.docid: 40975
negative_passages.text: Quotient of the ring of integers of a number field by a prime ideal
negative_passages.docid: 131497
negative_passages.text: Maximal ideal not containing the set of powers of an element is prime
negative_passages.docid: 108896
negative_passages.text: Prime ideal in a polynomial ring over an integrally closed domain
negative_passages.docid: 129302
negative_passages.text: Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
negative_passages.docid: 53801
negative_passages.text: Why are powers of coprime ideals are coprime?
negative_passages.docid: 67669
negative_passages.text: Prime ideals of a finite direct product ring
negative_passages.docid: 138882
negative_passages.text: A prime poset of ideals
negative_passages.docid: 116883
negative_passages.text: About ideals in a ring which is a $k$ vector space
negative_passages.docid: 75558
negative_passages.text: Counter-example for prime ideals in a non commutative ring.
negative_passages.docid: 93641
negative_passages.text: A maximal ideal among those avoiding a multiplicative set is prime
negative_passages.docid: 19230
negative_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
negative_passages.docid: 92519
negative_passages.text: ideal behind Maximal ideals are Prime ideals
negative_passages.docid: 74370
negative_passages.text: $P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$
negative_passages.docid: 97740
negative_passages.text: Homogeneous ideals are contained in homogeneous prime ideals
negative_passages.docid: 85206
negative_passages.text: Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
negative_passages.docid: 135586
negative_passages.text: Prove that the preimage of a prime ideal is also prime.