16.2.11. Let a Z(2) = {re Q|r=, with a, b € Z, gcd (a,b) = 1, and b odd}. In other words, any rational number whose denominator, when written in reduced form, is odd is in Z(2). The operations for Z(2) are the usual addition and multiplication of rational numbers. (a) Is Z(2) a ring? An integral domain? A field? (b) What are the units of Z(2)? (c) What is (3)? What is ()? What is (2)? (d) Can you find a maximal ideal in Z(2)? Give a proof that the ideal that you are suggesting is actually maximal. (e) Can you identify Z(2)/(2)?