query: Question involving the homomorphism theorem.
positive_passages.docid: 148616
positive_passages.text: When is a ring homomorphism $A \to A$ surjective but not injective.
negative_passages.docid: 2153
negative_passages.text: How to get a homomorphism from $\mathbb{Z}\to G$, for $G$ a non-trivial group?
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: 154847
negative_passages.text: homomorphism from $S_3$ to $\mathbb Z/3\mathbb Z$
negative_passages.docid: 26661
negative_passages.text: Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
negative_passages.docid: 63447
negative_passages.text: Prove that the kernel of a homomorphism is a principal ideal. (Artin, Exercise 9.13)
negative_passages.docid: 131946
negative_passages.text: Order of an Element Under a Homomorphism
negative_passages.docid: 117897
negative_passages.text: A homomorphism induces a continuous map from ${\rm Spec}(A') \to {\rm Spec}(A)$.
negative_passages.docid: 112131
negative_passages.text: Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
negative_passages.docid: 106347
negative_passages.text: Why is the image of a homomorphism a subgroup of the codomain?
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: 36980
negative_passages.text: Prove the third isomorphism theorem
negative_passages.docid: 48818
negative_passages.text: Homomorphism of local rings
negative_passages.docid: 47623
negative_passages.text: The set of all complex homomorphisms of abelian group $G$ has the same structure as $G$
negative_passages.docid: 40383
negative_passages.text: Is it true that $|g| = |\phi(g)|$ for all homomorphisms $\phi: G \to G$ and $g \in G$?
negative_passages.docid: 22995
negative_passages.text: Let f:G to H be 1-1 homomorphism show that order of f(a) divides the order of G.
negative_passages.docid: 84132
negative_passages.text: Number of preimages of a group element under a homomorphism.