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Proceedings of the London Mathematical Society 2005 91(1):105-128; doi:10.1112/S0024611504015151
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© London Mathematical Society

Large Lattices Over Orders

Wolfgang Rump

Institut für Algebra und Zahlentheorie, Universität Stuttgart Pfaffenwaldring 57, D–70550 Stuttgart, Germany. E-mail: rump{at}mathematik.uni-stuttgart.de

Received 3 March 2004. Revision received 5 October 2004.

Let K be the quotient field of a Dedekind domain R. We characterize the R-orders {Lambda} in a separable K-algebra for which every R-projective {Lambda}-module decomposes into {Lambda}-lattices. Butler, Campbell and Kovács have recently shown that the latter holds for the integral group ring of a cyclic group of prime order, as well as for lattice-finite orders over a complete discrete valuation domain. 2000 Mathematics Subject Classification 16H05, 16G30 (primary), 05C65 (secondary).

Key Words: large lattice • decomposition • lattice-finite • hypergraph


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