Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ACTIONS OF FINITE-DIMENSIONAL SEMISIMPLE HOPF ALGEBRAS AND INVARIANT ALGEBRAS

  • Min, Kang-Ju (Department of Mathematics, Chungnam National University) ;
  • Park, Jun-Seok (Department of Mathematics, Hoseo University)
  • Published : 1998.04.01
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Abstract

Let H be a finite dimensional Hopf algebra over a field k, and A be an H-module algebra over k which the H-action on A is D-continuous. We show that $Q_{max}(A)$, the maximal ring or quotients of A, is an H-module algebra. This is used to prove that if H is a finite dimensional semisimple Hopf algebra and A is a semiprime right(left) Goldie algebra than $A#H$ is a semiprime right(left) Goldie algebra. Assume that Asi a semiprime H-module algebra Then $A^H$ is left Artinian if and only if A is left Artinian.

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References

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