Can anyone help me with the problems below, it's very urgent.
1. R is a ring with property that x^2=x for each x in R.
a) Show that each element of R equals its own negative. (Hint: Consider (x+x)^2)
b) Hence show that R is a commutative ring.
2. Find a factorisation of 9+4sqrt(3) into irreducibles, in Z[sqrt(3)]
Thank you for your input.