Consider $Z_5$ and $Z_{20}$ as ring modulo 5 and 20 respectively..Then number of homomorphism $φ:Z_5 \to Z_{20}$ is a)1 b)2 c)4 d)5 since $Z_5$ and $Z_{20}$ is also group then number of group homomorphism is g.c.d of $(5,20)=5$ again if we consider ring homomorphism then number of ring homomorphism is 2.so in this case which option I will chose.I am totally confused.
Consider Z5 and Z20 as ring modulo 5 and 20 respectively..Then number of homomorphism φ:Z5 to Z20
1
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group-theory
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0Ring homomorphisms usually send 1 to 1. If that is the case for you, then there is at most one ring homomorphism. – 2017-01-06
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1I think it is trivial ring homomorphism – 2017-01-06
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1the number of ring homomorphsm from Zm to Zn is 2^{W(n)-W(g.c.d of (m,n))}.where w(n) is number of prime divisor of n.so there are 2 ring homomorphism ,1 ois trivial and other is non-trivial ring homomorphism – 2017-01-06
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1$Bbb Z_5$ has no proper ideals so the homomorphism is either injective or trivial. If $1$ is mapped to $1$ then what happens to $1+1+1+1+1$? – 2017-01-06