Degree upper bounds for H-Bases

Abstract

The main objective of this paper is to present upper bounds for the degree of H-bases of polynomial ideals. For this purpose, we introduce the new concept of  reduced H-bases and show that the maximal degree of the elements of any reduced H-basis of an ideal is independent of the choice of the basis. Furthermore, we show that, given an ideal, this maximal degree is invariant after performing any linear change of variables on the ideal. These results allow us to establish explicit degree upper bounds in the case of either a zero-dimensional ideal or an ideal generated by a regular sequence.