The syzygy theorem for Bézout rings

Gamanda, Maroua; Lombardi, Henri; Neuwirth, Stefan; Yengui, Ihsen

doi:10.1090/mcom/3466

The syzygy theorem for Bézout rings
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by Maroua Gamanda, Henri Lombardi, Stefan Neuwirth and Ihsen Yengui HTML | PDF

Math. Comp. 89 (2020), 941-964

Abstract:

We provide constructive versions of Hilbert’s syzygy theorem for $\mathbb {Z}$ and $\mathbb {Z}/N\mathbb {Z}$ 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.

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