Abstract
In this work, we propose a method for computing noncommutative Gröbner bases over a noetherian valuation ring. We have generalized the fundamental theorem on normal forms over an arbitrary ring. The classical method of dynamical commutative Gröbner bases is generalized to Buchberger's algorithm over R = 𝒱 ⟨ x 1,…, x m ⟩, a free associative algebra with noncommuting variables, where 𝒱 = ℤ/nℤ and 𝒱 = ℤ.
The proposed process generalizes previous known techniques for the computation of commutative Gröbner bases over a nætherian valuation ring and/or noncommutative Gröbner bases over a field.
ACKNOWLEDGMENT
The first author is grateful to the IMU Berlin Einstein Foundation, the Berlin Mathematical School, and to Pr. Dr. Klaus Altmann for receiving him in Berlin during the writing of a part of this paper.
Notes
Communicated by A. Elduque.