On the Coradical Filtration of Pointed Coalgebras
نویسنده
چکیده
We investigate the coradical filtration of pointed coalgebras. First, we generalize a theorem of Taft and Wilson using techniques developed by Radford in [Rad78] and [Rad82]. 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.
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