Year: 2012
Type: preprint
Abstract: In this work, it is proposed a method for computing Noncommutative Gröbner bases over a valuation nœtherian ring. We have generalized the fundamental theorem on normal forms over an arbitrary ring. The classical method of dynamical commutative Gröbner bases is generalized for Buchberger's algorithm over $R=\mathcal{V}$ 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 Gröbner bases over a valuation nœtherian ring and/or Noncommutative Gröbner bases over a field.
Source: arXiv (Cornell University)
Authors: Bouesso, André Mialebama, Sow, Djiby
Institution: Cheikh Anta Diop University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950285848