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Prove subring and field of quotients?

  1. Jun 11, 2012 #1
    How do I show that the set D= { a/b in Q | such that b is not divisible by 5} is a subring of Q. Find the field of quotients (field of fractions) of D.
    ( Q is the set of rational numbers.)

    Thank you.
  2. jcsd
  3. Jun 11, 2012 #2
    To check that it's a subring, I think you need to check closure under addition and multiplication, and check that it contains 0 and 1.

    To find the field of fractions, notice it is a subset of Q, that it contains Z, and recall what the field of fractions for Z is.

    Though you might prefer to try a more hands on approach in finding the field of fractions, to exercise your understanding of the concepts.

    Also, while I mentioned how you might find the field of fractions, proving what the field of fractions is will require a good argument.
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