  Two criteria for a closed connected definite 4-manifold with infinite cyclic
fundamental group to be TOP-split are given. One criterion extends a sufficient
condition made in a previous paper. The result is equivalent to a purely
algebraic result on the question asking when a positive definite Hermitian form
over the ring of integral one-variable Laurent polynomials is represented by an
integer matrix. As an application, an infinite family of orthogonally
indecomposable unimodular odd definite symmetric $Z$-forms is produced.
