Details:
Title  Value monoids of zerodimensional valuations of rank 1  Author(s)  Edward Mosteig  Type  Article in Journal  Abstract  Classically, Gröbner bases are computed by first prescribing a fixed monomial order. Moss Sweedler suggested an alternative in the mid1980s and developed a framework for performing such computations by using valuation rings in place of monomial orders. We build on these ideas by providing a class of valuations on K(x, y) that are suitable for this framework. We then perform such computations for ideals in the polynomial ring K[x ,y] . Interestingly, for these valuations, some ideals have finite Gröbner bases with respect to a valuation that are not Gröbner bases with respect to any monomial order, whereas other ideals only have Gröbner bases that are infinite.  Keywords  Valuations, Gröbner bases  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717108000151 
Language  English  Journal  Journal of Symbolic Computation  Volume  43  Number  10  Pages  688  725  Year  2008  Edition  0  Translation 
No  Refereed 
No 
