query: Prove that a certain ideal $I$ of $\mathbb Z [x]$ is not a principal ideal.
positive_passages.docid: 1720
positive_passages.text: Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
negative_passages.docid: 122012
negative_passages.text: The ideal $(x,y)$ is not a free $K[x,y]$-module
negative_passages.docid: 70856
negative_passages.text: Construct ideals in $\mathbb Z[x]$ with a given least number of generators
negative_passages.docid: 69352
negative_passages.text: Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
negative_passages.docid: 92703
negative_passages.text: Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
negative_passages.docid: 81982
negative_passages.text: Is $\mathbb{Z}[x]$ a principal ideal domain?
negative_passages.docid: 17075
negative_passages.text: Show an Ideal is the principal ideal for some polynomial.
negative_passages.docid: 57310
negative_passages.text: Prove $\mathbb{Z}$ is not a vector space over a field
negative_passages.docid: 53367
negative_passages.text: In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
negative_passages.docid: 33245
negative_passages.text: Show that every ideal of the ring $\mathbb Z$ is principal
negative_passages.docid: 19230
negative_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
negative_passages.docid: 104486
negative_passages.text: Ideal in $\mathbb Z[x]$ which is not two-generated
negative_passages.docid: 94747
negative_passages.text: Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
negative_passages.docid: 93029
negative_passages.text: Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
negative_passages.docid: 138114
negative_passages.text: Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
negative_passages.docid: 114640
negative_passages.text: Showing that an ideal is not a free $R-$module.
negative_passages.docid: 76501
negative_passages.text: How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?