On indecomposable definite hermitian forms

In this paper, for any given natural numbersn anda, we can construct explicitly positive definite indecomposable integral Hermitian forms of rankn over with discriminanta, with the following ten exceptions:n=2,a=1, 2, 4, 10;n=3,a=1, 2, 5;n=4,a=1;n=5,a=1; andn=7,a=1. In the exceptional cases there are no forms with the desired properties. The method given here can be applied to solving the problem of constructing indecomposable positive definite HermitianR _m -lattices of any given rankn and discriminanta, whereR _m is the ring of algebraic integers in an imaginary quadratic field with class number unity.