5
$\begingroup$

How to describe all ring homomorphism from $\mathbb Z \times \mathbb Z \to \mathbb Z$ ?

  • 0
    What is $Z*Z$ ?2010-11-15
  • 0
    the product of Z and Z2010-11-15
  • 1
    For 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
  • 1
    The 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

3 Answers 3