
Commutative Ring
My professor gave us this query at the end of class, and I started thinking about axioms, but I didn't think of anything that would have to make the following statement true. Thoughts?
What must be true about a nontrivial commutative ring R in order to conclude
(a+b)^4 = a^4 + 2a^2b^2 + b^4 for all elements a and b in R?
Clarification would be great on this one.

Note that by the binomial theorem,
$\displaystyle (a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4$
If the ring has characteristic 4, that is, $\displaystyle 4x=0$ for all $\displaystyle x\in R$, then this would simplify to
$\displaystyle a^4+2a^2b^2+b^4$

So that just means it has to be characteristic 4?