query: Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
positive_passages.docid: 1686
positive_passages.text: Show that quotient rings are not isomorphic
negative_passages.docid: 6171
negative_passages.text: Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
negative_passages.docid: 17859
negative_passages.text: Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
negative_passages.docid: 25050
negative_passages.text: To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
negative_passages.docid: 79056
negative_passages.text: Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
negative_passages.docid: 64130
negative_passages.text: Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
negative_passages.docid: 155642
negative_passages.text: Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
negative_passages.docid: 42552
negative_passages.text: Localisation is isomorphic to a quotient of polynomial ring
negative_passages.docid: 87101
negative_passages.text: Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
negative_passages.docid: 88474
negative_passages.text: $\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
negative_passages.docid: 117590
negative_passages.text: Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal
negative_passages.docid: 74537
negative_passages.text: Maximal Ideals in $K[y]$
negative_passages.docid: 137983
negative_passages.text: Normalisation of $k[x,y]/(y^2-x^2(x-1))$
negative_passages.docid: 122012
negative_passages.text: The ideal $(x,y)$ is not a free $K[x,y]$-module
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
negative_passages.docid: 67796
negative_passages.text: How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
negative_passages.docid: 94747
negative_passages.text: Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.