- #1

silvermane

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## Homework Statement

Inside the rational numbers Q, let's say we have a collection of all fractions where they all have an odd denominator. Prove that this collection is a subring of Q.

## The Attempt at a Solution

I know that a ring is a set, R, with two operations, + and *, and two special elements, 0 and 1, that satisfy:

1.) R with the operation + is a group with identity 0, called the zero element of R. The element b so that a+b = b+a = 0 is the negative of a.

2.) R with the operation * satisfies the associative property, and the element 1 is the identity element under multiplication.

3.) R with + and * satisfies the distributive laws: for every a, b, c in R, a(b+c) = (ab)+(ac), and (a+b)c = (ac) + (bc).

I know these are some of the rules, but I don't know if I just have to show that these are true for our set {..., -1/5,-1/3, -1, 0 , 1, 1/3, 1/5, ...} or if there are more to show. Any helpful hints or tips would be well appreciated!

Thank you for your help in advance!