oh ok. We actually are doing rings before groups so I would not have been able to use groups that is why i resorted to using units.
Thanks for confirming my answer!
Homework Statement
Explain why Z4 x Z4 is not isomorphic to Z16.
Homework Equations
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) ...
Homework Statement
Let f: R -> S be a homomorphism of Rings and T a subring of S.
Let P = { r belongs to R | f(r) belongs to T}
Prove P is a subring of R.
Homework Equations
Theorems used:
If S and nonempty subset of R such that S is closed under multiplication and addition, then...