Tame objects for finite commutative Hopf algebras
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- by William C. Waterhouse PDF
- Proc. Amer. Math. Soc. 103 (1988), 354-356 Request permission
Abstract:
Let $S$ be an $A$-module algebra for a commutative Hopf algebra $A$, both projective of the same rank over a commutative ring. Let ${\mathbf {I}}$ be the space of integrals in $A$. Then $S$ is an invertible $A$-module iff it is a faithful module which satisfies the "trace surjectivity" condition that 1 is in ${\mathbf {I}}S$.References
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N. Bourbaki, Algèbre commutative, Chapitre 1, 2, Hermann, Paris, 1961.
- Lindsay N. Childs and Susan Hurley, Tameness and local normal bases for objects of finite Hopf algebras, Trans. Amer. Math. Soc. 298 (1986), no. 2, 763–778. MR 860392, DOI 10.1090/S0002-9947-1986-0860392-3
- Bodo Pareigis, When Hopf algebras are Frobenius algebras, J. Algebra 18 (1971), 588–596. MR 280522, DOI 10.1016/0021-8693(71)90141-4
- Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 354-356
- MSC: Primary 13B05; Secondary 16A24
- DOI: https://doi.org/10.1090/S0002-9939-1988-0943044-8
- MathSciNet review: 943044