On the coradical filtration of pointed coalgebras

We investigate the coradical filtration of pointed coalgebras. First, we generalize a theorem of Taft and Wilson using techniques developed by Radford. We then look at the coradical filtration of duals of inseparable field extensions L* upon extension of the base field K, where K L is a field extension. We reduce the problem to the case that the field extension is purely inseparable. We use this to prove that if E is a field containing the normal closure of L over K, then E L*=(E L*)1 if and only if L/K is separable or char(K)=L:Ls=2, where Ls is the separable closure of K in L.