Semiperfect coalgebras over rings
نویسنده
چکیده
Our investigation of coalgebras over commutative rings R is based on the close relationship between comodules over a coalgebra C and modules over the dual algebra C∗. If C is projective as an R-module the category of right C-comodules can be identified with the category σ[C∗C] of left C∗-modules which are subgenerated by C. In this context semiperfect coalgebras are described by results from module theory. Over QF rings semiperfect coalgebras are characterized by the exactness of the trace functor Tr(σ[C∗C],−).
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