Generalised Buchberger and Schreyer algorithms for strongly discrete coherent rings

Autor:	Neuwirth, Stefan, Lombardi, Henri, Yengui, Ihsen
Rok vydání:	2024
Předmět:	Mathematics - Commutative Algebra
Druh dokumentu:	Working Paper
Popis:	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. Comment: arXiv admin note: text overlap with arXiv:1905.08117
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.16460 Zobrazit plný text záznamu View this record from Arxiv