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arXiv · 2411.16460

Generalised Buchberger and Schreyer algorithms for strongly discrete coherent rings

Stefan Neuwirth·Henri Lombardi·Ihsen Yengui
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Abstract

Let M be a finitely generated submodule of a free module over a multivariate polynomial ring with coefficients in a discrete coherent ring. We prove that its module MLT(M ) of leading terms is countably generated and provide an algorithm for computing explicitly a generating set. This result is also useful when MLT(M ) is not finitely generated. Suppose that the base ring is strongly discrete coherent. We provide a Buchberger-like algorithm and prove that it converges if, and only if, the module of leading terms is finitely generated. We also provide a constructive version of Hilbert's syzygy theorem by following Schreyer's method.

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Stefan Neuwirth, Henri Lombardi, Ihsen Yengui. 2024-11-25. Generalised Buchberger and Schreyer algorithms for strongly discrete coherent rings. https://arxiv.org/abs/2411.16460

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