query: Is there an integral domain containing an element having no factorization into irreducible elements?
positive_passages.docid: 102914
positive_passages.text: Integral domain that is not a factorization domain
negative_passages.docid: 97902
negative_passages.text: In a integral domain every prime element is irreducible
negative_passages.docid: 87101
negative_passages.text: Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
negative_passages.docid: 154845
negative_passages.text: Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
negative_passages.docid: 14158
negative_passages.text: Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
negative_passages.docid: 43103
negative_passages.text: Unique factorization domain and principal ideals
negative_passages.docid: 74139
negative_passages.text: Subrings of integral domains have the same identity element.
negative_passages.docid: 153069
negative_passages.text: Proof for Unique Factorization Domain
negative_passages.docid: 83871
negative_passages.text: GCDs in integral domains are unique up to unit factors (associates)
negative_passages.docid: 114480
negative_passages.text: Example of a domain where all irreducibles are primes and that is not a GCD domain
negative_passages.docid: 108767
negative_passages.text: Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition
negative_passages.docid: 49303
negative_passages.text: In a noetherian integral domain every non invertible element is a product of irreducible elements
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: 20612
negative_passages.text: Is fibre product of varieties irreducible (integral)?
negative_passages.docid: 75899
negative_passages.text: Principal ideal domain with finitely many ideals
negative_passages.docid: 123024
negative_passages.text: A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
negative_passages.docid: 121845
negative_passages.text: Quotient of polynomials, PID but not Euclidean domain?