query: Prove or disprove that the ring $\mathbb{Z}[x]/(x^2-1)$ is an integral domain
positive_passages.docid: 133636
positive_passages.text: Is $\mathbb Z[X]/(X^2-1)$ a domain?
negative_passages.docid: 81982
negative_passages.text: Is $\mathbb{Z}[x]$ a principal ideal domain?
negative_passages.docid: 119699
negative_passages.text: Examples of Cohen-Macaulay integral domains
negative_passages.docid: 119702
negative_passages.text: Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$
negative_passages.docid: 148550
negative_passages.text: Units in quotient ring of $\mathbb Z[X]$
negative_passages.docid: 94579
negative_passages.text: $\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
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: 157488
negative_passages.text: Proving that $k[x,y,z]/(xz - (y^2 + 1))$ is a normal ring.
negative_passages.docid: 17859
negative_passages.text: Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
negative_passages.docid: 67699
negative_passages.text: Integral domain that is integrally closed, one-dimensional and not noetherian
negative_passages.docid: 87617
negative_passages.text: Ring of $\mathbb{Z}_2$-valued functions
negative_passages.docid: 7903
negative_passages.text: Prove that $B[x] \cap B[x^{-1}]$ is integral over $B$
negative_passages.docid: 31933
negative_passages.text: $x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
negative_passages.docid: 35279
negative_passages.text: It's $\mathbb{Z}\subseteq \mathbb{Z}[X]/(X^5-1)$ an integral extension?
negative_passages.docid: 154845
negative_passages.text: Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
negative_passages.docid: 25397
negative_passages.text: Prove $R \times R$ is NOT an integral domain
negative_passages.docid: 13174
negative_passages.text: Show that $A[X]/(aX+b)$ is an integral domain