On Primitive Representations by Unimodular Quadratic Z2-Lattices

Necessary and sufficient conditions are given for the primitive representations of an odd quadratic Z2-lattice M with rank m by an odd unimodular quadratic Z2-lattice L with rank n for m+m(1)= n, where m(1)is the rank of a sublattice M(1) of M for a Jordan decomposition M = M(0)⊥M(1) with M(0)unimodular and B(M(1),M(1))⊆2Z2 for the associated bilinear form B.