Basic Results on Ideals and Varieties in Finite Fields
Roger Germundsson · 1991
: The connection between ideals and varieties for polynomial rings over finite fields is investigated. An extension to Hilbert's Nullstellen Satz is given for these ideals. Furthermore projections and embeddings of these is examined. These results basically give ideal theoretic formulations for several algebro-geometric questions. This in turn is translated to Grobner basis and polynomial remainder calculations. An example implementation in Mathematica is also given. Keywords: Ideal, Variety, Algebraic Geometry, Grobner Basis, Nullstellen Satz, Commutative Algebra 1 Introduction This report basically clarifies the relation between algebro-geometric objects such as variety and homomorphisms and projections thereof to their corresponding ideals. It might seem strange to have such a report coming from an electrical engineering department, but basically we were following another track, namely finite systems defined by polynomials over finite fields. As the standard algebraic geometry or ...