query: For ring homomorphism $\phi:R\to S$, prove that $\phi(R)$ is a subring of $S$.
positive_passages.docid: 149856
positive_passages.text: Image of ring homomorphism is a subring
negative_passages.docid: 126930
negative_passages.text: Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
negative_passages.docid: 67237
negative_passages.text: Pull back image of maximal ideal under surjective ring homomorphism is maximal
negative_passages.docid: 15000
negative_passages.text: Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
negative_passages.docid: 75315
negative_passages.text: How to prove that homomorphism from field to ring is injective or zero?
negative_passages.docid: 7890
negative_passages.text: Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
negative_passages.docid: 5802
negative_passages.text: Proving the universal mapping property for polynomial rings
negative_passages.docid: 115541
negative_passages.text: Subrings of polynomial rings over the complex plane
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: 45627
negative_passages.text: Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$
negative_passages.docid: 6171
negative_passages.text: Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
negative_passages.docid: 143451
negative_passages.text: Homomorphism from $(\Bbb Q,+)$ to a finite group
negative_passages.docid: 48818
negative_passages.text: Homomorphism of local rings
negative_passages.docid: 44396
negative_passages.text: Noetherian Ring under a Homomorphism / homomorphic function / map
negative_passages.docid: 97605
negative_passages.text: Let $f$ be a surjective homomorphism. Prove that $\ker(f)$ is a maximal ideal
negative_passages.docid: 13764
negative_passages.text: Homomorphisms from $\mathbb{Z} \rightarrow S_3$.
negative_passages.docid: 157585
negative_passages.text: Structure theorem of finite rings