Strassmann's theorem
From Wikipedia, the free encyclopedia
In mathematics, Strassman's theorem is a result in field theory. It states that, for suitable fields, suitable formal power series with coefficients in the valuation ring of the field have only finitely many zeroes.
[edit] Statement of the theorem
Let K be a field with a non-Archimedean absolute value | · | and let R be the valuation ring of K. Let f(x) be a formal power series with coefficients in R other than the zero series, with coefficients an converging to zero with respect to | · |. Then f(x) has only finitely many zeroes in R.
[edit] References
- Murty, M. Ram (2002). Introduction to P-Adic Analytic Number Theory. American Mathematical Society, 35. ISBN 978-0-8218-3262-2.
