کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
401880 676738 2008 38 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Value monoids of zero-dimensional valuations of rank 1
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
Value monoids of zero-dimensional valuations of rank 1
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 43, Issue 10, October 2008, Pages 688-725