Algebra and Topology Seminar

4pm Tuesday 7 February 2006
Michael Butler
University of Liverpool

Rump's criterion for full decomposability of all generalised lattices over a classical order

Let R be a Dedekind domain, K its field of quotients, A a separable K-algebra, and S an R-order in A. A generalised lattice (lattice) over S is defined to be an S-module which is projective (and finitely generated) as an R-module. I will discuss W. Rump's recent description of orders S over which all generalised lattices decompose as direct sums of lattices, and in the particular case of the integral group rings S = ZG where |G| = 6, will indicate why this property holds for the dihedral group but not for the cyclic group.




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