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Homework Statement
Let G = \{a + b\sqrt{2} | a,b \in \mathbb{Q}\}
(a)Show that G is a group under addition
(b)Show that G - {0} is a group undermultiplication.
The Attempt at a Solution
I think this problem should be easy if I could get on the right start.
(a) All I know is to prove that G is a group is to show it is associative, has an identity, and has inverses under addition. The problem is I have no clue where to start since I have never seen this before. I am guessing I should let a = \frac{m}{n} and b = \frac{k}{l}. Now how do I go about showing this is associative? Don't I need an extra element, say c, to show that it is associative? If so, can I just arbitrarily create one?
Thank you and any help is greatly appreciated.