Signature Gröbner bases in free algebras over rings
Clemens Hofstadler, Thibaut Verron · 2023
We generalize signature Gröbner bases, previously studied in the free algebra over a field or polynomial rings over a ring, to ideals in the mixed algebra R[x1, …, xk]⟨y1, …, yn⟩ where R is a principal ideal domain. We give an algorithm for computing them, combining elements from the theory of commutative and noncommutative (signature) Gröbner bases, and prove its correctness.