query: Intersection of two principal ideals in an integral domain.
positive_passages.docid: 16727
positive_passages.text: Intersection of finitely generated ideals
negative_passages.docid: 119699
negative_passages.text: Examples of Cohen-Macaulay integral domains
negative_passages.docid: 111189
negative_passages.text: Intersection of all maximal ideals containing a given ideal
negative_passages.docid: 104789
negative_passages.text: How to tell an ideal of integer polynomial ring is principal?
negative_passages.docid: 145594
negative_passages.text: Splitting of prime ideals in algebraic extensions
negative_passages.docid: 41347
negative_passages.text: The dimension of the intersection of two vector subspaces
negative_passages.docid: 5360
negative_passages.text: Ideal contained in a finite union of prime ideals
negative_passages.docid: 110984
negative_passages.text: Ideals and prime ideals in a commutative ring.
negative_passages.docid: 94819
negative_passages.text: Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.
negative_passages.docid: 65536
negative_passages.text: Finitely generated ideals in a Boolean ring are principal, why?
negative_passages.docid: 67944
negative_passages.text: Nilpotent Elements and Intersection of Prime Ideals
negative_passages.docid: 47134
negative_passages.text: Ideals generated by two elements
negative_passages.docid: 90314
negative_passages.text: Maximal ideals in $R[x]$
negative_passages.docid: 3604
negative_passages.text: If F is a field, then $F[x,y]$ is a Principal Ideal Domain?
negative_passages.docid: 74796
negative_passages.text: Extension of intersection of ideals
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: 130156
negative_passages.text: Image of the union and intersection of sets.