ordered fields and abstract algebra?
How can we show that R := Z[x,y]/<x^2 - 2y^2> is a discretely ordered ring? (In this case, the orderings are free to choose)
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How can we show that R := Z[x,y]/<x^2 - 2y^2> is a discretely ordered ring? (In this case, the orderings are free to choose)
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I don't think it is...
It has been a long time since I took group theory, but ...
You will need to show that your opperation is comutative, and transative, etc.
show that:
a,b = b,a
There exists and identity I such that a,I = a for all a.
If a>b and c>I then a,c > b,c
if a>I and b>I then a,b >I