English

An algorithm for computing syzygies on $V[X]$ when $V$ is a valuation domain

Commutative Algebra 2024-04-11 v1

Abstract

We give an algorithm for computing the V-saturation of any finitely-generated submodule of a power of V[X], where V is a valuation domain. Our algorithm is based on a notion of "echelon form" which ensures its correctness. This allows us to compute a finite system of generators for the syzygy module of any finitely generated submodule of a power of V[X].

Keywords

Cite

@article{arxiv.2304.00303,
  title  = {An algorithm for computing syzygies on $V[X]$ when $V$ is a valuation domain},
  author = {Henri Lombardi and Claude Quitté and Ihsen Yengui},
  journal= {arXiv preprint arXiv:2304.00303},
  year   = {2024}
}

Comments

4 figures

R2 v1 2026-06-28T09:44:34.150Z