Algebraic series and valuation rings over nonclosed fields

Details Algebraic series and valuation rings over nonclosed fields Algebraic series and valuation rings over nonclosed fields

2007-10-29

arxiv.org/abs/0710.5522v3

Mathematics

Commutative Algebra

17 pages; final version to appear in JPAA

Scientific paper

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 $\sigma$ 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 $\sigma$ 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 $R$.

Affiliated with

Also associated with

No associations

Rating

Algebraic series and valuation rings over nonclosed fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Algebraic series and valuation rings over nonclosed fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Algebraic series and valuation rings over nonclosed fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-364668