Gr\"obner bases of modules over sigma-PBW extensions
Haydee Jim\'enez, Oswaldo Lezama
TL;DR
This paper extends the theory of Gr"obner bases from left ideals to modules over sigma-PBW extensions, enabling computation of syzygies in specific algebraic structures.
Contribution
It generalizes Gr"obner bases theory to modules over sigma-PBW extensions and provides methods to compute syzygies in bijective quasi-commutative cases.
Findings
Extended Gr"obner bases theory to modules over sigma-PBW extensions.
Developed algorithms for computing syzygies in bijective quasi-commutative sigma-PBW extensions.
Abstract
For sigma-PWB extensions, we extend to modules the theory of Gr\"obner bases of left ideals presented in [5]. As an application, if A is a bijective quasi-commutative sigma-PWB extension, we compute the module of syzygies of a submodule of the free module A^m.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Rings, Modules, and Algebras