Large lattices over orders

Abstract

Let K be the quotient field of a Dedekind domain R. We characterize the R-orders Λ in a separable K-algebra for which every R-projective Λ-module decomposes into Λ-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).