Minimal Homogeneous Bases for Polynomial Ideals

The minimal homogeneous basis is defined. It is shown that every minimal homogeneous basis of an ideal has the same number of elements. An algorithm for finding a minimal homogeneous basis is developed. The main idea is to modify the classical Buchbergers algorithm for finding a Gröbner basis so that a minimal homogeneous basis can be obtained as a subset of a Gröbner basis.