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Math Help - How to prove something is a subring

  1. #1
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    How to prove something is a subring

    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?
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  2. #2
    Super Member girdav's Avatar
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    I think you have to prove that if a,b \in S, a+b\in S and a\cdot b\in S.
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