Please help with the following problems.
a) If I,J are ideals in a ring R such that I+J=R and R is isomorphic to the product ring (R/I)x(R/J) when IJ=0, describe the idempotents corresponding to this product decomposition;
b) Describe the maximal ideal of RxR where in this case R is the set of real numbers;
c) How many roots does x^2-2 have, modulo 8?