Hello all!

I was looking over some examples of congruence classes and I ran into one I could not find.

1.Is there/Are therea congruence class(es) $\displaystyle (mod (3+\sqrt{3})/2) $ in $\displaystyle Q[\sqrt{-3}] $ ? If so, what are they? I'm not sure if they exist or not even.

2. If $\displaystyle \alpha $ is a quadratic integer in $\displaystyle Q[\sqrt{-d}] $, then a notion of congruence $\displaystyle (mod \alpha) $ can be defined.can this be defined how can we further define +, -, and x for congruences classes?How

Thank you everyone!

-Samson