query: Showing there are no nontrivial ring homomorphisms from $\mathbb{Z}\to\mathbb{Z}$
positive_passages.docid: 144105
positive_passages.text: Ring homomorphism from $\mathbb Z$ to $\mathbb Z$ is always identity or $0$
negative_passages.docid: 94747
negative_passages.text: Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
negative_passages.docid: 64025
negative_passages.text: Ring homomorphisms from $\Bbb Q$ into a ring
negative_passages.docid: 98731
negative_passages.text: Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
negative_passages.docid: 153291
negative_passages.text: Why a ring homomorphism from a local ring will not map a non-unit to a unit？
negative_passages.docid: 34990
negative_passages.text: Ring homomorphism defined on a field
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: 76391
negative_passages.text: What are all the homomorphisms between the rings $\mathbb{Z}_{18}$ and $\mathbb{Z}_{15}$?
negative_passages.docid: 642
negative_passages.text: Does a surjective ring homomorphism have to be surjective on the unit groups?
negative_passages.docid: 92211
negative_passages.text: When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
negative_passages.docid: 26749
negative_passages.text: $\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
negative_passages.docid: 141984
negative_passages.text: Find the number of homomorphisms between $\mathbb{Z}_m$ and $\mathbb{Z}_n$
negative_passages.docid: 64048
negative_passages.text: Describe all ring homomorphisms
negative_passages.docid: 101064
negative_passages.text: Showing the triviality of homomorphisms
negative_passages.docid: 152306
negative_passages.text: Finding homomorphisms from $\mathbb Z_{12}$ to $\mathbb Z_{6}$.
negative_passages.docid: 146341
negative_passages.text: Finding all ring homomorphisms from a field to itself
negative_passages.docid: 5906
negative_passages.text: All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $