Generalized coderivations of bicomodules

摘要

We introduce a generalized coderivation from a bicomodule to a bicomodule over corings, which is a generalization of a coderivation. For each (D, C)-bicomodule N over corings C and D, we construct the universal generalized coderivation υ_N : U(N) → N such that every generalized coderivation from a (D, C)-bicomodule M to N is uniquely expressed as υ_N of with some (D, C)-bicomodule map f : M → U(N). U(N) is isomorphic to the cotensor product of N and U(D (direct×)_r C). We show that a coring C is cosep-arable if and only if, for any coring D, all generalized coderivations from a (D, C)-bicomodule to a (D,C)-bicomodule are inner.