query: Intersection of two principal ideals in an integral domain.
positive_passages.docid: 147722
positive_passages.text: Is there a nice example of integral domain $R$ and $s,t \in R$, with $Rs \cap Rt$ not principal but lcm($s,t$) exists?
negative_passages.docid: 123024
negative_passages.text: A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
negative_passages.docid: 145594
negative_passages.text: Splitting of prime ideals in algebraic extensions
negative_passages.docid: 587
negative_passages.text: Ideal Generated by the Union of Two Ideals
negative_passages.docid: 80679
negative_passages.text: Principal ideal rings that are not integral domains
negative_passages.docid: 49854
negative_passages.text: Ideals in polynomial rings generated by linear polynomials
negative_passages.docid: 134939
negative_passages.text: Norm of element $\alpha$ equal to absolute norm of principal ideal $(\alpha)$
negative_passages.docid: 16727
negative_passages.text: Intersection of finitely generated ideals
negative_passages.docid: 85915
negative_passages.text: Principal prime ideals are minimal among prime ideals in a UFD
negative_passages.docid: 129371
negative_passages.text: Maximal ideals in the ring of real functions on $[0,1]$
negative_passages.docid: 22789
negative_passages.text: How to determine whether a unique factorization domain is a principal ideal domain?
negative_passages.docid: 141410
negative_passages.text: Injective integral domains are fields
negative_passages.docid: 17075
negative_passages.text: Show an Ideal is the principal ideal for some polynomial.
negative_passages.docid: 89271
negative_passages.text: If $F$ is a field, then $F[x]$ is a principal ideal domain proof question
negative_passages.docid: 68167
negative_passages.text: Intersection of powers of an ideal in a Noetherian ring
negative_passages.docid: 96787
negative_passages.text: Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?
negative_passages.docid: 81743
negative_passages.text: Prime ideals in $C[0,1]$