Explain why Z4 x Z4 is not isomorphic to Z16.
Going to talk about units in a ring.
Units are properties preserved by isomorphism.
The Attempt at a Solution
We see the only units in Z4 are 1 and 3.
So the units of Z4 x Z4 are (1,1) , (3,3) , (1,3) , (3,1)
The Units of Z16 are 1,3,5,7,9,11,13,15.
So there are 4 units in Z4 x Z4 but in Z16 we have 8 units. So there can not be an isomorphism between the two.
Is this correct?