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A Characterization of Group Rings as a Special Class of Hopf Algebras
Published online by Cambridge University Press: 20 November 2018
Extract
By a group ring we mean in this paper a ring defined by a finite group G and an integral domain K:
such that A contains G and is freely generated by G over K, so that
The ring A = KG has a co-multiplication
defined by
so that A is a Hopf algebra.
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- Copyright © Canadian Mathematical Society 1965
References
1) In particular J. L. Kelley, Duality for compact groups, Proc. N. A. S. 49 (1963) pp. 457-458.
*) The author would like to thank Professor Geoffrey Fox and the referee for their valuable suggestions.
2) We follow the presentation of S. MacLane, Homology, 1963, pp. 197-198.
3) Always commutative with the identity 1.
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