query: How to prove that $\mathbb{Z}[X]/g\mathbb{Z}[X]$ is not a field?
positive_passages.docid: 17991
positive_passages.text: Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
negative_passages.docid: 41035
negative_passages.text: Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
negative_passages.docid: 98731
negative_passages.text: Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
negative_passages.docid: 82485
negative_passages.text: Show that the set of non zero rationals is not a cyclic group under multiplication.
negative_passages.docid: 23879
negative_passages.text: If $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$
negative_passages.docid: 95764
negative_passages.text: Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
negative_passages.docid: 135611
negative_passages.text: Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
negative_passages.docid: 124864
negative_passages.text: A not free $\mathbb{Z}$-module
negative_passages.docid: 19310
negative_passages.text: Identify the ring $\mathbb{Z}[x]/(2x)$
negative_passages.docid: 104486
negative_passages.text: Ideal in $\mathbb Z[x]$ which is not two-generated
negative_passages.docid: 73248
negative_passages.text: Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group
negative_passages.docid: 158502
negative_passages.text: Showing $\sin(\bar{z})$ is not analytic at any point of $\mathbb{C}$
negative_passages.docid: 69046
negative_passages.text: Proof of $\mathbb{Q}$ is not cyclic
negative_passages.docid: 155745
negative_passages.text: Ideals of $\mathbb{Z}[X]$
negative_passages.docid: 46565
negative_passages.text: Show that $\mathbb{Q}(\sqrt{2})$ is a field.
negative_passages.docid: 33781
negative_passages.text: Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
negative_passages.docid: 76501
negative_passages.text: How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?