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TitleValue monoids of zero-dimensional valuations of rank 1
Author(s) Edward Mosteig
TypeArticle in Journal
AbstractClassically, 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.
KeywordsValuations, Gröbner bases
URL http://www.sciencedirect.com/science/article/pii/S0747717108000151
JournalJournal of Symbolic Computation
Pages688 - 725
Translation No
Refereed No