Abstract
Let S S be an A A -module algebra for a commutative Hopf algebra A A , both projective of the same rank over a commutative ring. Let I {\mathbf {I}} be the space of integrals in A A . Then S S is an invertible A A -module iff it is a faithful module which satisfies the "trace surjectivity" condition that 1 is in I S {\mathbf {I}}S .
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