  In this work, it is proposed a method for computing Noncommutative Gr\"obner
bases over a valuation n{\oe}therian ring. We have generalized the fundamental
theorem on normal forms over an arbitrary ring. The classical method of
dynamical commutative Gr\"obner bases is generalized for Buchberger's algorithm
over $R=\mathcal{V}<x_1,...,x_m>$ a free associative algebra with non-commuting
variables, where $\mathcal{V}=\mathbb{Z}/n\mathbb{Z}$ or
$\mathcal{V}=\mathbb{Z}$.
  The process proposed, generalizes previous known technics for the computation
of Commutative Gr\"obner bases over a valuation n{\oe}therian ring and/or
Noncommutative Gr\"obner bases over a field.
