Essential and inessential elements of a standard basis

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