How to describe all ring homomorphism from $\mathbb Z \times \mathbb Z \to \mathbb Z$ ?
All homomorphisms from the ring $\mathbb Z \times \mathbb Z \to \mathbb Z$
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ring-theory
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0What is $Z*Z$ ? – 2010-11-15
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0the product of Z and Z – 2010-11-15
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1For a map $\varphi:\mathbb{Z}\times \mathbb{Z}\rightarrow \mathbb{Z}$, look at $\varphi(1,0), \;\varphi(0,1)$. what are the conditions on them so that $\varphi$ would be a ring homomorphism? – 2010-11-15
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1The direct product of rings $R$ and $S$ is denoted by $R\times S$, not by $R*S$. For your question, note that under a ring homomorphism, idempotents go to idempotents. – 2010-11-15