Some topics on hom_A(M, –) in the category of relative hopf modules

Abstract

Let H be a Hopf algebra over a field k,A a right H-comodule algebra and the category of relative Hopf modules. For let HOM _A (M, N) be the k-subspace of Hom _A (M, N) defined by Ulbrich. We shall prove that for a co-Frobenius Hopf algebra H, HOM A(M,N) is dense in Hom _A (M,N) with respect to the finite topology (Theorem 2.2). For if and only if M is small as a right A-moduie (Theorem 3.7). These two theorems generalize results of Pardo and Nastasescu and Pardo, Milita.ru and N[acaron]st[acaron]sescu for the case H = k[G].