query: The ideal $\langle x,y \rangle$ in $F[x,y]$ is not principal.
positive_passages.docid: 20296
positive_passages.text: The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
negative_passages.docid: 18484
negative_passages.text: Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
negative_passages.docid: 146801
negative_passages.text: Primary decomposition of an ideal
negative_passages.docid: 17991
negative_passages.text: Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
negative_passages.docid: 78143
negative_passages.text: Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
negative_passages.docid: 36078
negative_passages.text: Example of a non invertible fractional ideal
negative_passages.docid: 144250
negative_passages.text: subideals of an ideal
negative_passages.docid: 156457
negative_passages.text: Show that $K[x,xy,xy^2,\dots]$ is not Noetherian
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: 104784
negative_passages.text: On the grade of an ideal
negative_passages.docid: 83050
negative_passages.text: Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
negative_passages.docid: 140553
negative_passages.text: An ideal which is not finitely generated
negative_passages.docid: 130367
negative_passages.text: Proof that $K\otimes_F L$ is not noetherian
negative_passages.docid: 122012
negative_passages.text: The ideal $(x,y)$ is not a free $K[x,y]$-module
negative_passages.docid: 18186
negative_passages.text: Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
negative_passages.docid: 104789
negative_passages.text: How to tell an ideal of integer polynomial ring is principal?
negative_passages.docid: 99198
negative_passages.text: Principal ideal and free module