Nilpotent elements in integral representation rings of Hopf-algebra orders in group algebras of prime order

Journal of Algebra (Impact Factor: 0.6). 12/1983; 85(2):410-423. DOI: 10.1016/0021-8693(83)90105-9


In this paper we shall find necessary and sufficient conditions for integral representation rings of Hopf-algebra orders to have non-zero nilpotent elements, when the order is a module over a discrete valuation ring, and an order in a group of prime order.

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    ABSTRACT: This survey considers work published between 1970 and 1990 on the algebraic aspects of Hopf theory. There are detailed discussions of the properties of antipodes, group and primitive elements, integrals, crossed products, Galois theory, Lie coalgebras, the category of Hopf algebras, quantum groups, etc.
    No preview · Article · Aug 1994 · Journal of Mathematical Sciences