"A Direct Products of Fields Approach to Comprehensive Gröbner Bases over Finite Fields"
, in Shirayanagi, K.: ACA 2005, Seite(n) 54--55, 8-2005, ISBN: 4-903027-02-3
A Direct Products of Fields Approach to Comprehensive Gröbner Bases over Finite Fields
Sprache des Titels:
We describe comprehensive Gröbner bases over finite fields by direct product of fields. In general, representatioins of comprehensive Gröbner bases have some conditions on parameters. However, in finite fields we can construct comprehensive Gröbner bases without conditions by the theory of von Neumann regular rings .\\ Alternative comprehensive Gröbner 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 Gröbner bases we are to describe are defined as Gröbner bases in polynomial rings over commutative von Neumann regular rings, hence the comprehensive Gröbner bases have some nice properties which we also describe.