Algebra Quiz

The least number of elements a nonzero M2(/2)-module can have is
The number of maximal ideals in [X,Y] containing {X2 + Y2, X2 - Y2} is
The order of the centralizer of an element of order 7 in a simple group of order 168 is
Let G be a group of order 8. Then the smallest number of two-sided ideals G can have is
The K denote the splitting field of X4 - 2 over . Then the number of elements of order 2 in Gal(K/(√2)) is

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