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TitleA Direct Products of Fields Approach to Comprehensive Grobner Bases over Finite Fields
Author(s) Katsusuke Nabeshima
TypeBook, Chapter in Book, Conference Proceeding
AbstractWe describe comprehensive Grobner bases over finite fields by direct product of fields. In general, representatioins of comprehensive Grobner bases have some conditions on parameters. However, in finite fields we can construct comprehensive Grobner bases without conditions by the theory of von Neumann regular rings. Alternative comprehensive Grobner bases (ACGB) are also bases on the theory of von Neumann regular rings. However, ACGB are defined for infinite fields, we can not use the method given by ACGB for finite fields. The comprehensive Grobner bases we are to describe are defined as Grobner bases in polynomial rings over commutative von Neumann regular rings, hence the comprehensive Grobner bases have some nice properties which we also describe.
EditorShirayanagi and K.
Translation No
Refereed No
ConferencenameACA 2005