query: injective ring homomorphism inducing a non-injective homomorphism?
positive_passages.docid: 28272
positive_passages.text: Does such localization of integral extension preserve inclusion?
negative_passages.docid: 5699
negative_passages.text: The number of ring homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$
negative_passages.docid: 119648
negative_passages.text: For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
negative_passages.docid: 151993
negative_passages.text: Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
negative_passages.docid: 51334
negative_passages.text: Does there exist any surjective group homomorphism from $(\mathbb R^* , .)$ onto $(\mathbb Q^* , .)$?
negative_passages.docid: 37058
negative_passages.text: Induced maps in homology are injective
negative_passages.docid: 68728
negative_passages.text: Why does the natural ring homomorphism induce a surjective group homomorphism of units?
negative_passages.docid: 140865
negative_passages.text: Rings' second isomorphism theorem
negative_passages.docid: 117897
negative_passages.text: A homomorphism induces a continuous map from ${\rm Spec}(A') \to {\rm Spec}(A)$.
negative_passages.docid: 144105
negative_passages.text: Ring homomorphism from $\mathbb Z$ to $\mathbb Z$ is always identity or $0$
negative_passages.docid: 45523
negative_passages.text: Can the product of two non invertible elements in a ring be invertible?
negative_passages.docid: 60760
negative_passages.text: Ring homomorphism and characteristic
negative_passages.docid: 133660
negative_passages.text: When can a homomorphism be determined entirely by its generators
negative_passages.docid: 97608
negative_passages.text: Showing a Ring of endomorphisms is isomorphic to a Ring
negative_passages.docid: 143884
negative_passages.text: A non-noetherian ring with noetherian spectrum
negative_passages.docid: 99567
negative_passages.text: Proving that an inverse ring homomorphism of an ideal is an ideal?
negative_passages.docid: 82559
negative_passages.text: Showing two ring homomorphisms that agree on the integers must agree on the rationals