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- Title
Nœther Bases and Their Applications.
- Authors
Hashemi, Amir; Parnian, Hossein; Seiler, Werner M.
- Abstract
In this paper, we introduce a new involutive division, called D-Nœther division, and the corresponding notion of a Nœther basis. It is shown that an ideal is in Nœther position, if and only if it possesses a finite Nœther basis. We present a deterministic algorithm which, given a homogeneous ideal, finds a linear change of variables so that the ideal after performing this change possesses a finite Nœther basis (and equivalently is in Nœther position). Furthermore, we define the new concept of an ideal of Nœther type and study its connections with Rees decompositions. We have implemented all the algorithms described in this paper in Maple and assess their performance on a number of benchmark examples.
- Subjects
GROBNER bases; POLYNOMIAL rings; DETERMINISTIC algorithms
- Publication
Bulletin of the Iranian Mathematical Society, 2019, Vol 45, Issue 5, p1283
- ISSN
1018-6301
- Publication type
Article
- DOI
10.1007/s41980-018-00198-9