Abstract
We examine valuations on a rational function field K(x, y) and analyze their behavior when restricting to an underlying polynomial ring . Motivated to solve the ideal membership problem in polynomial rings using Moss Sweedler’s framework of generalized Gröbner bases, we produce an infinite collection of valuations such that is reversely well ordered. In addition, we construct a surprising example where is nonpositive, yet not reversely well ordered.
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