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Jun7-06, 11:13 AM
Uh? Why are you defining L(a) like that? L is the map of A/N to A/N, it sends cosets to cosets L[a]=[alpha(a)], and is obviously an isometry:
(L([a],L[b])= f(alpha(a)*alpha(b)) = f(a*b) hence is an isometry.