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Noncommutative Gröbner Bases over Rings

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 $R=\mathcal{V}\langle x_1,\ldots,x_m\rangle$ 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.


Auteur(s) : André Saint Eudes Mialebama Bouesso & Djiby Sow
Pages : 541-557
Année de publication : 2015
Revue : Communications in Algebra
N° de volume : 43:2
Type : Article
Mise en ligne par : SOW Djiby