  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.
