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TitleStrong Noether position and stabilized regularities.
Author(s) Amir Hashemi
TypeArticle in Journal
AbstractIn this article, we introduce the notion of a homogeneous ideal in strong Nœther position (SNP); a new definition for the notion of generic coordinates for some problems. This definition is simple to check, because it can be tested on the initial ideal for the degree reverse lexicographic ordering. It is explicit, because we provide an algorithm to decide whether a monomial ideal is in SNP or not. To any notion of regularity of an ideal (Castelnuovo–Mumford regularity, satiety, maximal degree of the elements of the reduced Gröbner basis with respect to the degree reverse lexicographic ordering, and Hilbert regularity), we associate a stabilized regularity. The main result of this article is that SNP shows simply and explicitly the relationships between these regularities.
KeywordsCastelnuovo–Mumford regularity, Generic coordinates, Gröbner basis, Hilbert regularity, Satiety
ISSN0092-7872; 1532-4125/e
URL http://www.tandfonline.com/doi/abs/10.1080/00927870902828546
JournalCommun. Algebra
PublisherTaylor & Francis, Philadelphia, PA
Translation No
Refereed No