query: Show that $R[x]/(x^2-c)$ is a Dedekind domain
positive_passages.docid: 108123
positive_passages.text: Why is $\mathbb{C}[x,y]/(y^2 - x^3 + 1)$ normal?
negative_passages.docid: 78380
negative_passages.text: Dedekind domain with a finite number of prime ideals is principal
negative_passages.docid: 154239
negative_passages.text: Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
negative_passages.docid: 113152
negative_passages.text: Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
negative_passages.docid: 155604
negative_passages.text: Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
negative_passages.docid: 5893
negative_passages.text: On the commutative property of multiplication (domain of integers, possibly reals)
negative_passages.docid: 90599
negative_passages.text: Trouble with proving $A$ is an integrally closed domain $\Rightarrow$ $A[t]$ is integrally closed domain
negative_passages.docid: 106911
negative_passages.text: Square root of $-1$ in the ring $\mathbb{R}[x]/\langle(x^2+1)^2\rangle$
negative_passages.docid: 85987
negative_passages.text: Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain
negative_passages.docid: 95146
negative_passages.text: Polynomial ring $R[X] $ has zero Jacobson radical, for $R$ a domain
negative_passages.docid: 57166
negative_passages.text: Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
negative_passages.docid: 90533
negative_passages.text: Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
negative_passages.docid: 13174
negative_passages.text: Show that $A[X]/(aX+b)$ is an integral domain
negative_passages.docid: 93621
negative_passages.text: Prove that $\mathbb{Z}[\omega]$ is an integral domain
negative_passages.docid: 111930
negative_passages.text: Domain of a Standard Parabola
negative_passages.docid: 141078
negative_passages.text: Domain over which a polynomial is strictly positive
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 $\mathbb Q(t)$