I think you have to prove that if , and .
In the rational numbers, Q, let S be the collection of all fractions that can be written with odd denominator. Prove S is a subring of Q.
What properties of rings and subrings do I need to prove to show that S is a subring? I think I will have to prove addition, multiplication, existence of a "0", and existence of a "1", but what else must I prove?