The number of non-trivial ring homomorphisms from $\mathbb{Z}_{12}$ to $\mathbb{Z}_{28}$ is (Options: a.1 b.3 c.4 d.7)
Ring homomorphism
6
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abstract-algebra
ring-theory
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6Let $f$ be such a homomorphism, what could be the value of $f(1)$ ? – 2012-09-22
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2A ring homomorphism preserving identity would have to send $\phi(0)=\phi(12)=12\neq 0$, so I'm beginning to suspect that we're talking about groups after all, or the ring homomorphisms do not have to preserve identity. – 2012-09-22