query: Is there any general formula for ring homomorphism if gcd$(p, q) \neq 1$?
positive_passages.docid: 5699
positive_passages.text: The number of ring homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$
negative_passages.docid: 149856
negative_passages.text: Image of ring homomorphism is a subring
negative_passages.docid: 144105
negative_passages.text: Ring homomorphism from $\mathbb Z$ to $\mathbb Z$ is always identity or $0$
negative_passages.docid: 60760
negative_passages.text: Ring homomorphism and characteristic
negative_passages.docid: 147667
negative_passages.text: Polynomial ring isomorphisms
negative_passages.docid: 123419
negative_passages.text: Abstract algebra: homomorphism and an element of a prime order
negative_passages.docid: 154847
negative_passages.text: homomorphism from $S_3$ to $\mathbb Z/3\mathbb Z$
negative_passages.docid: 5223
negative_passages.text: $\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$
negative_passages.docid: 2208
negative_passages.text: $\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
negative_passages.docid: 59566
negative_passages.text: Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
negative_passages.docid: 129858
negative_passages.text: "Almost" ring homomorphism
negative_passages.docid: 7938
negative_passages.text: Number of Homomorphisms from $\Bbb{Z}_m$ to $\Bbb{Z}_n$
negative_passages.docid: 151993
negative_passages.text: Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
negative_passages.docid: 97999
negative_passages.text: Explain these ring isomorphisms
negative_passages.docid: 111743
negative_passages.text: In a ring homomorphism we always have $f(1)=1$?
negative_passages.docid: 43155
negative_passages.text: Cyclotomic Polynomials and GCD
negative_passages.docid: 40383
negative_passages.text: Is it true that $|g| = |\phi(g)|$ for all homomorphisms $\phi: G \to G$ and $g \in G$?