Strongly Rational Comodules and Semiperfect Hopf Algebras over QF Rings
نویسندگان
چکیده
Let C be a coalgebra over a QF ring R. A left C-comodule is called strongly rational if its injective hull embeds in the dual of a right Ccomodule. Using this notion a number of characterizations of right semiperfect coalgebras over QF rings are given, e.g., C is right semiperfect if and only if C is strongly rational as left C-comodule. Applying these results we show that a Hopf algebra H over a QF ring R is right semiperfect if and only if it is left semiperfect or equivalently the (left) integrals form a free R-module of rank 1.
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