|Title||Basic results on ideals and varieties in finite fields|
|Author(s)|| Roger Germundsson|
|Text||R. Germundsson. Basic results on ideals and varieties in finite fields.
Technical Report LiTH-ISY-I-1259, Dept. of Electrical Engineering, Linkoping University, S-581 83 Linkoping, Sweden, September 1991.|
|Type||Technical Report, Misc|
|Abstract||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, Gröbner basis, Nullstellen Satz, commutative algebra|