تقرير
Computing Gr\'obner Bases and Free Resolutions of OI-Modules
| العنوان: | Computing Gr\'obner Bases and Free Resolutions of OI-Modules |
|---|---|
| المؤلفون: | Morrow, Michael, Nagel, Uwe |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Commutative Algebra |
| الوصف: | Given a sequence of related modules $M_n$ defined over a sequence of related polynomial rings, one may ask how to simultaneously compute a finite Gr\"obner basis for each $M_n$. Furthermore, one may ask how to simultaneously compute the module of syzygies of each $M_n$. In this paper we address both questions. Working in the setting of OI-modules over a Noetherian polynomial OI-algebra, we provide OI-analogues of Buchberger's Criterion, Buchberger's Algorithm for computing Gr\"obner bases, and Schreyer's Theorem for computing syzygies. We also establish a stabilization result for Gr\"obner bases. Comment: 16 pages; some modifications |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2303.06725 |
| رقم الأكسشن: | edsarx.2303.06725 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |