Canonical representatives for residue classes of a polynomial ideal

Abstract

At the EUROSAM Conference 1974 it was conjectured that there exist probably no canonical forms for polynomial expressions under polynomial side relations. In 1965, however, Buchberger had already implemented a reduction algorithm solving the problem over fields. Positive results were also attained independently since 1974 by R. Shtokhamer and the author. In this note a general theorem on canonical representatives is obtained and by application to Buchberger's and Shtokhamer's algorithms it is proven that the stated problem is solved.