Algebraic series and valuation rings over nonclosed fields
| dc.creator | Cutkosky, Steven Dale | |
| dc.creator | Kashcheyeva, Olga | |
| dc.date | 2007-10-29 | |
| dc.date | 2008-01-07 | |
| dc.date.accessioned | 2026-07-07T08:52:31Z | |
| dc.date.available | 2026-07-07T08:52:31Z | |
| dc.description | Suppose that $k$ is an arbitrary field. Consider the field $k((x_1,...,x_n))$, which is the quotient field of the ring $k[[x_1,...,x_n]]$ of formal power series in the variables $x_1,...,x_n$, with coefficients in $k$. Suppose that $σ$ is a formal power series in $x_1,...,x_n$ with coefficints in the algebraic closure of $k$. We give a very simple necessary and sufficient condition for $σ$ to be algebraic over $k((x_1,...,x_n))$. As an application of our methods, we give a characterization of valuation rings $V$ which dominate an excellent, Noetherian local domain $R$ of dimension two, and such that the rank increases after passing to the completion of a birational extension of $R$. | |
| dc.description | 17 pages; final version to appear in JPAA | |
| dc.identifier | https://arxiv.org/abs/0710.5522 | |
| dc.identifier | http://arxiv.org/abs/0710.5522 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145303 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13J05 (Primary); 13A18 (Secondary) | |
| dc.title | Algebraic series and valuation rings over nonclosed fields | |
| dc.type | text |