Hey everybody, thank you for reading.

I have an exam soon, and I have accumulated some questions which I haven't found a solution for... I'd appreciate it if I could get a push...

1)Given a ring in which every x in R satisfies x^3=x, I need to show it's commutative, and fail to see why. (note: this question was given a little after teaching the basic definitions and notions of "ideals".)

2) Given a set which is almost a ring, besides the fact that we're not given that a+b=b+a (abelian group under addition), thathas a unit element, I need to show that the condition a+b=b+a must be satisfied anyhow.

'note: there's a hint here: expand (a+b)(1+1) in 2 ways. Haven't mannaged to do anything with that, however.

That's it for now :-)

Thanks!!!

Tomer.