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Abstract
In this article, we introduce the σ-PWB extensions and construct the theory of Gröbner bases for the left ideals of them. We prove the Hilbert's basis theorem and the division algorithm for this more general class of Poincaré–Birkhoff–Witt extensions. For the particular case of bijective and quasi-commutative σ-PWB extensions, we implement the Buchberger's algorithm for computing Gröbner bases of left ideals.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The authors are grateful to the editors and the referee for valuable suggestions and corrections.
The first author was sponsored by Vicerrectoría Académica UN.
The second author was partially supported by DIB-UN, project 8003130.
Notes
Communicated by D. Zacharia.