Integrality of Module Algebras over Its Invariants Original Research Article

LetKbe a field andHbe a finite dimensional Hopf algebra overK. IfHis cocommutative, then it is known that all commutativeH-module algebras are integral over its invariants. Here we prove this result for those Hopf algebrasHsuch that eitherHis involutionary with Char Kdoes not dividedim HorHhas a cocommutative coradical andKis of positive characteristic. Examples are constructed to illustrate that the conclusion is not true, in general.