Prove subring and field of quotients?

[katherine1124]

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.

 

[algebrat]

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.