query: Can the prime ideals of $A_a$ be identified with those prime ideals of $A$ which do not contain $a$?
positive_passages.docid: 17247
positive_passages.text: Localisation and prime ideals
negative_passages.docid: 94157
negative_passages.text: Normal Ring and Prime Ideal whose Square is Principal
negative_passages.docid: 133975
negative_passages.text: Localising a polynomial ring and non-maximal prime ideal
negative_passages.docid: 116453
negative_passages.text: Is any quotient of a Euclidean domain by a prime ideal a Euclidean domain?
negative_passages.docid: 31585
negative_passages.text: Primary ideals of $\mathbb{Z}$
negative_passages.docid: 139334
negative_passages.text: Determining the existence or non-existence of Non Trivial Ideals of $L(V)$
negative_passages.docid: 129302
negative_passages.text: Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
negative_passages.docid: 50809
negative_passages.text: Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
negative_passages.docid: 91180
negative_passages.text: Show $R \setminus S$ is a union of prime ideals
negative_passages.docid: 252
negative_passages.text: Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
negative_passages.docid: 23099
negative_passages.text: Verifying that the ideal $(x^3-y^2)$ is prime
negative_passages.docid: 137858
negative_passages.text: Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
negative_passages.docid: 67203
negative_passages.text: Complement of maximal multiplicative set is a prime ideal
negative_passages.docid: 81743
negative_passages.text: Prime ideals in $C[0,1]$
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: 63171
negative_passages.text: Translate of an ideal by $a$ coincides with the ideal iff  $a \in I$
negative_passages.docid: 154239
negative_passages.text: Can a prime in a Dedekind domain be contained in the union of the other prime ideals?