  Assume that we are given a semifree noncommutative differential graded
algebra (DGA for short) whose differential respects an action filtration. We
show that the canonical unital algebra map from the homology of the DGA to its
characteristic algebra, i.e. the quotient of the underlying algebra by the
two-sided ideal generated by the boundaries, is a monomorphism. The main tool
that we use is the weak division algorithm in free noncommutative algebras due
to P. Cohn.
