English

Essential and inessential elements of a standard basis

Commutative Algebra 2010-01-12 v1

Abstract

In this paper we introduce the concept of inessential element of a standard basis of I, where I is any homogeneous ideal of a polynomial ring. An inessential element is, roughly speaking, a form of the basis whose omission produces an ideal having the same saturation of I; it becomes useless in any dehomogenization of I with respect to a linear form. We study the properties of the basis linked to the presence of inessential elements and give some examples.

Keywords

Cite

@article{arxiv.1001.1694,
  title  = {Essential and inessential elements of a standard basis},
  author = {Giannina Beccari and Carla Massaza},
  journal= {arXiv preprint arXiv:1001.1694},
  year   = {2010}
}

Comments

15 pages

R2 v1 2026-06-21T14:33:13.506Z