On Indecomposable Definite Unimodular Hermitian Forms

(整期优先)网络出版时间:1994-02-12
/ 1
<正>Foranynaturalnumbersmandn≥17wecanconstructexplicitlyindecomposabledefiniteunimodularnormalHermitianlatticesofranknovertheringofalgebraicintegersRminanimaginaryquadraticfield(-m1/2).Itisprovedthatforanyn(incasem=11,thereisoneexceptionn=3)thereexistindecomposabledefiniteunimodularnormalHermitianR15(R11-latticesofrankn,andweexhibitrepresentativesforeachclass.Intheexceptionalcasetherearenolatticeswiththedesiredproperties.ThemethodgiveninthispapercansolvecompletelytheproblemofconstructingindecomposabledefiniteunimodularnormalHermitianRm-latticesofanyranknforeachm.