Value monoids of zero-dimensional valuations of rank 1

• Autores: Edward Mosteig
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 43, Nº 10, 2008, págs. 688-725
• Idioma: inglés
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• Resumen

  • Classically, Gröbner bases are computed by first prescribing a fixed monomial order. Moss Sweedler suggested an alternative in the mid-1980s 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.