query: Intersection of Ideals of coprime elements in a UFD
positive_passages.docid: 127030
positive_passages.text: Simple example of non-arithmetic ring (non-distributive ideal lattice)
negative_passages.docid: 56800
negative_passages.text: Intersection of prime ideals
negative_passages.docid: 90314
negative_passages.text: Maximal ideals in $R[x]$
negative_passages.docid: 49854
negative_passages.text: Ideals in polynomial rings generated by linear polynomials
negative_passages.docid: 36150
negative_passages.text: Ideal in a ring of continuous functions
negative_passages.docid: 93686
negative_passages.text: In a UFD, lcm = product for coprimes: $\,(a,b)=1,\ a,b\mid c\Rightarrow ab\mid c$
negative_passages.docid: 83798
negative_passages.text: Does $A$ a UFD imply that  $A[T]$ is also a UFD?
negative_passages.docid: 112045
negative_passages.text: A property of minimal prime ideal
negative_passages.docid: 587
negative_passages.text: Ideal Generated by the Union of Two Ideals
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: 72350
negative_passages.text: Constructing Idempotent Generator of Idempotent Ideal
negative_passages.docid: 108896
negative_passages.text: Prime ideal in a polynomial ring over an integrally closed domain
negative_passages.docid: 60391
negative_passages.text: Ideal Generated by Three Elements in Polynomial Ring
negative_passages.docid: 63736
negative_passages.text: Every radical ideal in a Noetherian ring is a finite intersection of primes
negative_passages.docid: 34183
negative_passages.text: An equivalent condition with $\{0\}$ being the only nilpotent ideal
negative_passages.docid: 74537
negative_passages.text: Maximal Ideals in $K[y]$
negative_passages.docid: 74558
negative_passages.text: Localization of ideals at all primes