On Indecomposable Positive Definite Integral Hermitian Forms

Let F=Q(i=m(i~2=-1, m>0 and square free) be an imaginary quadratic field and Rits ring of algebraic integers. The aim of this note is to construct n-ary positive definite indecomposable integral. Hermitian forms over Rwith given rank and given discriminant. The word decomposition or splitting is the geometric one, i. e. lattice L has a non-trivial expression of the form L=M⊥N. If there is no such expression we call L indecomposable. There is another kind of decomposition——a more algebraic one. A positive definite Hermitian form