query: Intersection of a nonzero prime ideal with a subring
positive_passages.docid: 16984
positive_passages.text: Finite extension of domains : preimage of non-zero ideal is non-zero?
negative_passages.docid: 19883
negative_passages.text: Prime ideals of the matrix ring
negative_passages.docid: 83100
negative_passages.text: Prove that the center of a ring is a subring.
negative_passages.docid: 41815
negative_passages.text: Galois extension of intersection of fields
negative_passages.docid: 5360
negative_passages.text: Ideal contained in a finite union of prime ideals
negative_passages.docid: 13901
negative_passages.text: Finitely many prime ideals lying over $\mathfrak{p}$
negative_passages.docid: 110022
negative_passages.text: Showing prime and maximal ideal
negative_passages.docid: 45484
negative_passages.text: Height unmixed ideal and a non-zero divisor
negative_passages.docid: 34807
negative_passages.text: Localization at finitely many minimal prime ideals
negative_passages.docid: 15904
negative_passages.text: Prime ideal and nilpotent elements
negative_passages.docid: 106550
negative_passages.text: The bijection between homogeneous prime ideals of $S_f$ and prime ideals of $(S_f)_0$
negative_passages.docid: 145594
negative_passages.text: Splitting of prime ideals in algebraic extensions
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 84386
negative_passages.text: Domain strictly contained in the intersection of localizations at the primes of height one
negative_passages.docid: 63568
negative_passages.text: Ring with finitely many zerodivisors
negative_passages.docid: 139334
negative_passages.text: Determining the existence or non-existence of Non Trivial Ideals of $L(V)$
negative_passages.docid: 144250
negative_passages.text: subideals of an ideal