A Characterization of Group Rings
作者:
Richard G. Larson,
期刊:
Communications in Algebra
(Taylor Available online 1974)
卷期:
Volume 1,
issue 1
页码: 65-78
ISSN:0092-7872
年代: 1974
DOI:10.1080/00927877408548609
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
In this paper we prove that every coseparable involutory Hopf algebra over the ring of integers Z which is a free Z-module is the group ring of some group. This result was proved independently for Hopf algebras which are finitely generated Z-modules by H.-J. Schneider [6], using similar techniques. We then give some examples of coseparable Hopf algebras over number rings which are not group algebras, and give an example of a cocommutative coseparable coalgebra over a number ring which cannot be given a multiplicative structure making it into a Hopf algebra. The Hopf algebra structure theory required for this paper is found in [1], [4], and [5]. For completeness we give proofs here of the coalgebra analogues to some “well-known” facts about separable algebras.
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