query: Need help in showing that $z\mapsto z^k$ is a surjective homomorphism.
positive_passages.docid: 27728
positive_passages.text: Question on a homomorphism of a set G.
negative_passages.docid: 40993
negative_passages.text: Let $f:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic.
negative_passages.docid: 143831
negative_passages.text: Showing $\mathbb{Q}$ is homeomorphic to $\mathbb{Q}^2$
negative_passages.docid: 6171
negative_passages.text: Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
negative_passages.docid: 16610
negative_passages.text: Surjectivity of a map from a space to itself
negative_passages.docid: 16092
negative_passages.text: How to prove that the composition of two surjective functions is surjective
negative_passages.docid: 45576
negative_passages.text: A surjective homomorphism between finite free modules of the same rank
negative_passages.docid: 32428
negative_passages.text: Group homomorphisms and which of the following statements are true (NBHM-$2014$)
negative_passages.docid: 13606
negative_passages.text: Prove that $K$ is isomorphic to a subfield of the ring of $n\times n$ matrices over $F$.
negative_passages.docid: 149856
negative_passages.text: Image of ring homomorphism is a subring
negative_passages.docid: 55900
negative_passages.text: Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
negative_passages.docid: 75315
negative_passages.text: How to prove that homomorphism from field to ring is injective or zero?
negative_passages.docid: 152306
negative_passages.text: Finding homomorphisms from $\mathbb Z_{12}$ to $\mathbb Z_{6}$.
negative_passages.docid: 57732
negative_passages.text: Rings of fractions and homomorphisms
negative_passages.docid: 62454
negative_passages.text: Let $f : G → G_1$ be a surjective homomorphism (also called epimorphism) from $G$ to another group $G_1$. Prove that $f(Z(G)) \subseteq Z(G_1)$.
negative_passages.docid: 119702
negative_passages.text: Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$
negative_passages.docid: 45991
negative_passages.text: Why $f\colon \mathbb{Z}_n^\times \to \mathbb{Z}_m^\times$ is surjective?