- #1
jakelyon
- 7
- 0
Can anyone tell me how many endomorphisms there are for Z/2Z? I think it is
two:
0 --> 0 and 1 --> 1
0 --> 0 and 1 --> 0
two:
0 --> 0 and 1 --> 1
0 --> 0 and 1 --> 0
A ring has two operations, addition and multiplication. So there are also two "identities": 0 is the neutral element with respect to addition, 1 is the neutral element with respect to multiplication. These are distinct, unless for the trivial ring. A ring homomorphism is a group homomorphism, and at the same time respects multiplication.I am thinking of group homomorphisms, so I know that it must map identities to identities. But I didn't think that it could only map identities to identities, thus not ruling out the second homomorphism.