# No of Homomorphisms

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• January 28th 2010, 08:22 PM
Chandru1
No of Homomorphisms
Find the no of ring homomorphisms $f: \mathbb{Z} \to \mathbb{Z}_{30}$
• January 29th 2010, 04:01 AM
NonCommAlg
Quote:

Originally Posted by Chandru1
Find the no of ring homomorphisms $f: \mathbb{Z} \to \mathbb{Z}_{30}$

Hint: look at $f(1).$ the number of ring homomorphisms is the number of roots of the equation $x^2=x$ in $\mathbb{Z}/30\mathbb{Z}.$