query: $\mathbb{R}[x,y]/(x^2+y^2-1)$ is integrally closed.
positive_passages.docid: 17859
positive_passages.text: Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
negative_passages.docid: 149971
negative_passages.text: Closed unit disk homeomorphic to $\mathbb{R}^2$?
negative_passages.docid: 108156
negative_passages.text: Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$
negative_passages.docid: 34177
negative_passages.text: Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
negative_passages.docid: 82900
negative_passages.text: Show that Minkowski sum of a closed set and a compact set in $\mathbb{R}^n$ is closed.
negative_passages.docid: 91682
negative_passages.text: Graph of a continuous function is closed
negative_passages.docid: 142901
negative_passages.text: "The closure of the unit ball of $C^1[0, 1]$ in $C[0, 1]$" and its compactness
negative_passages.docid: 10180
negative_passages.text: How to prove that this set is closed?
negative_passages.docid: 108123
negative_passages.text: Why is $\mathbb{C}[x,y]/(y^2 - x^3 + 1)$ normal?
negative_passages.docid: 21599
negative_passages.text: $(0,1)$ is an open subset of $\mathbb{R}$ but not of $\mathbb{R}^2$, when we think of $\mathbb{R}$ as the x-axis in $\mathbb{R}^2$. Prove this.
negative_passages.docid: 20539
negative_passages.text: Differential form is closed if the integral over a curve is rational number.
negative_passages.docid: 60614
negative_passages.text: Why is it that Complex Numbers are algebraically closed?
negative_passages.docid: 143457
negative_passages.text: Is product of two closed sets closed?
negative_passages.docid: 46622
negative_passages.text: Let $ Y = \{ (1,1),(0,0\} \subset \mathbb A_k^2$. Find the $ \mathbb I(Y)$.
negative_passages.docid: 137983
negative_passages.text: Normalisation of $k[x,y]/(y^2-x^2(x-1))$
negative_passages.docid: 8317
negative_passages.text: Understanding a proof of "If $R$ is an integral domain, then $R[x]$ is an integral domain as well".
negative_passages.docid: 131082
negative_passages.text: Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic