The syzygy theorem for Bézout rings
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 Bézout rings with a divisibility test for the case of finitely generated modules whose module of leading terms is finitely generated.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.08117
- arXiv:
- arXiv:1905.08117
- Bibcode:
- 2019arXiv190508117G
- Keywords:
-
- Mathematics - Commutative Algebra;
- 13D02;
- 13P10;
- 13C10;
- 13P20;
- 14Q20
- E-Print:
- 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