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Computing Leading Exponents of Noetherian Power Series
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mosteig, Edward |
| Copyright Year | 2002 |
| Abstract | For a field k of characteristic zero, we study the field of Noetherian power series, k〈〈tQ〉〉, which consists of maps z : Q → k whose supports are Noetherian (i.e., reverse well-ordered) subsets of Q. There is a canonical valuation LE : k〈〈tQ〉〉 → Q ∪ {−∞} that sends a nonzero series to the maximum element of its support. Given a nonzero polynomial f(x, y) ∈ k[x, y] and a series z ∈ k〈〈tQ〉〉 that is transcendental over k(t), we construct a formula for LE(f(t, z)) in terms of the roots of f(t, y) ∈ k(t)[y]. Using this formula, we find sufficient conditions for {LE(f(t, z)) : f(x, y) ∈ k[x, y]} to be a well-ordered subset of Q. In particular, this set is well-ordered in case the support of z consists solely of positive numbers. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://myweb.lmu.edu/faculty/emosteig/research/lexp.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Map Plant Roots Polynomial Subgroup Value (ethics) |
| Content Type | Text |
| Resource Type | Article |
