Buchberger and Schreyer algorithms are generalized to strongly discrete coherent rings, with convergence characterized by finite generation of the leading term module.
The syzygy theorem for B\'ezout rings
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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.
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Generalised Buchberger and Schreyer algorithms for strongly discrete coherent rings
Buchberger and Schreyer algorithms are generalized to strongly discrete coherent rings, with convergence characterized by finite generation of the leading term module.