English

The syzygy theorem for B\'ezout rings

Commutative Algebra 2024-01-31 v4

Abstract

We provide constructive versions of Hilbert's syzygy theorem for Z and Z/nZ following Schreyer's method. Moreover, we extend these results to arbitrary coherent strict B\'ezout rings with a divisibility test for the case of finitely generated modules whose module of leading terms is finitely generated.

Keywords

Cite

@article{arxiv.1905.08117,
  title  = {The syzygy theorem for B\'ezout rings},
  author = {Maroua Gamanda and Henri Lombardi and Stefan Neuwirth and Ihsen Yengui},
  journal= {arXiv preprint arXiv:1905.08117},
  year   = {2024}
}

Comments

This version differs from the published version for the statement and proof of Theorem 5.5, the statement of Theorems 5.8 and 6.2, as well as the free resolution at the end of Example 6.7. The changes have been typeset in green