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Consider $Z_{20}$ and $Z_{44}$ as ring modulo $20$ and $44$ respectively.Then number of non-trivial ring homomorohism from $Z_{20}$ to $Z_{44}$ is?

Harsh Kumar
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Arib khan
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    Well, $f(1)=1$, so $f(1+1)=f(1)+f(1)=1+1$, $\ldots$ – vadim123 Dec 31 '16 at 15:11
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    Generally, visitors to this site like to know what a questioner already knows about the field, and what ideas have been tried, successfully or unsuccessfully. – Lubin Dec 31 '16 at 15:29
  • Ring homomorphisms usually send 1 to 1. If that is the case for you, then there is at most one ring homomorphism – lhf Jan 06 '17 at 11:04

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The number of ring homomorphism from $Z_m$ to $Z_n$ is $2^{W(n)-W(n/g.c.d(m,n))}$ where $W(n)$ is number of prime divisor of $n$. so number of ring homomorphism is 2..out of 2 1 is trivial homomorphism so 1 is non-trivial homomorphism..

YuiTo Cheng
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Halima.Khatun
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