Rees algebras and gröbner bases

Abstract

I-34100-Trieste (Italy). This paper deals with the following problem. Robbiano showed in [9] that standard bases, Grobner bases, Macaulay bases are all instances of the same general situation. In this paper, we develop this philosophy from the point of view of the Rees algebra R of a ring A w.r.t. a filtration F given on A. The ring R plays a fine job between A and the graded ring G associated to (A, F). The use of R and the properties of termorderings and their relate Grobner bases led naturally to the definition of Grobner filtrations in general commutative rings.