query: Proof question: Show there is no homomorphism from $\Bbb Z_{16} \oplus \Bbb Z_{2}$ onto $\Bbb Z_4 \oplus \Bbb Z_4$
positive_passages.docid: 109987
positive_passages.text: No homomorphism from $Z_{16}\oplus Z_{2}$ onto $Z_{4}\oplus Z_{4}$.
negative_passages.docid: 108955
negative_passages.text: Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
negative_passages.docid: 1026
negative_passages.text: Ring homomorphism with $\phi(1_R) \neq1_S$
negative_passages.docid: 75315
negative_passages.text: How to prove that homomorphism from field to ring is injective or zero?
negative_passages.docid: 125604
negative_passages.text: Proof that $\mathbb{Z}$ has no zero divisors
negative_passages.docid: 97258
negative_passages.text: Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$
negative_passages.docid: 129162
negative_passages.text: Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$
negative_passages.docid: 46342
negative_passages.text: Prove that $G$ is abelian iff $\varphi(g) = g^2$ is a homomorphism
negative_passages.docid: 78048
negative_passages.text: Group of order 24 with no element of order 6 is isomorphic to $S_4$
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: 113216
negative_passages.text: No field properly between $\mathbb Q$ and $E$ iff $G(K/\mathbb Q) \cong A_4$ or $S_4$
negative_passages.docid: 1720
negative_passages.text: Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
negative_passages.docid: 91222
negative_passages.text: Isomorphism between $\mathfrak o(4,\mathbb R)$ and $\mathfrak o (3,\mathbb R) \oplus\mathfrak o (3,\mathbb R) $
negative_passages.docid: 146969
negative_passages.text: Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
negative_passages.docid: 33455
negative_passages.text: Question on group homomorphisms involving the standard Z-basis
negative_passages.docid: 137029
negative_passages.text: Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.
negative_passages.docid: 90433
negative_passages.text: Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$