Document Type
Article - post-print
Publication Date
2008
Abstract
Classically, Grobner bases are computed by first prescribing a set monomial order. Moss Sweedler suggested an alternative and developed a framework to perform 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. For these valuations, we compute ν(k[x, y] ∗ ) and use this to perform computations concerning ideals in the polynomial ring k[x, y]. Interestingly, for these valuations, some ideals have a finite Grobner basis with respect to the valuation that is not a Grobner basis with respect to any monomial order, whereas other ideals only have Grobner bases that are infinite with respect to the valuation.
Original Publication Citation
Edward Mosteig, Value monoids of zero-dimensional valuations of rank 1, Journal of Symbolic Computation, Volume 43, Issue 10, 2008, Pages 688-725, http://dx.doi.org/10.1016/j.jsc.2008.01.005.
Publisher Statement
This is an author-manuscript of an article accepted for publication in Journal of Symbolic Computation following peer review. The version of record: Edward Mosteig, Value monoids of zero-dimensional valuations of rank 1, Journal of Symbolic Computation, Volume 43, Issue 10, 2008, Pages 688-725, is available online at: http://dx.doi.org/10.1016/j.jsc.2008.01.005.
Digital Commons @ LMU & LLS Citation
Mosteig, Edward, "Value Monoids Of Zero-Dimensional Valuations Of Rank 1" (2008). Mathematics, Statistics and Data Science Faculty Works. 79.
https://digitalcommons.lmu.edu/math_fac/79
