query: If R is an integral domain disprove the RxR is an integral domain?
positive_passages.docid: 25397
positive_passages.text: Prove $R \times R$ is NOT an integral domain
negative_passages.docid: 77877
negative_passages.text: Is there a domain "larger" than (i.e., a supserset of) the complex number domain?
negative_passages.docid: 141410
negative_passages.text: Injective integral domains are fields
negative_passages.docid: 84189
negative_passages.text: Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
negative_passages.docid: 13174
negative_passages.text: Show that $A[X]/(aX+b)$ is an integral domain
negative_passages.docid: 133636
negative_passages.text: Is $\mathbb Z[X]/(X^2-1)$ a domain?
negative_passages.docid: 35569
negative_passages.text: Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
negative_passages.docid: 74330
negative_passages.text: $\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
negative_passages.docid: 123024
negative_passages.text: A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
negative_passages.docid: 81982
negative_passages.text: Is $\mathbb{Z}[x]$ a principal ideal domain?
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: 97902
negative_passages.text: In a integral domain every prime element is irreducible
negative_passages.docid: 24351
negative_passages.text: The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
negative_passages.docid: 13983
negative_passages.text: Show that If $R[X]$ is Euclidean domain then $R$ is a field
negative_passages.docid: 139463
negative_passages.text: Commutative integral domain does not finitely generate its field of fractions
negative_passages.docid: 551
negative_passages.text: Why is a finite integral domain always field?
negative_passages.docid: 95146
negative_passages.text: Polynomial ring $R[X] $ has zero Jacobson radical, for $R$ a domain