Let P = {ab : a,b Z and b is odd}. This forms a commutative ring with the usual addition and subtraction of rational numbers. Let Q = {ab : a,b Z, a is even, and b is odd}. Then Q is an ideal of P. Prove that Q is a maximal ideal of P.

Let P = {2^x(a/b)|x in N, a,b are odd}

1. Show that all ideals of P are {0} or 2^xP for x>=0

2. Show that for x>0, then 2^xP subset of 2^(x-1)P

Q= 2P