MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Hi, I am looking for examples of non-discrete valuation rings. Could you help me? Thanks

share|cite|improve this question

closed as off topic by Martin Brandenburg, Qiaochu Yuan, Sándor Kovács, Mark Sapir, Ben Webster Feb 2 '11 at 21:20

Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.

Please read the FAQ; this question does not seem to be appropriate for MO. Anyway I give you a hint: Open a book which treats valuation rings, there are many examples. – Martin Brandenburg Feb 2 '11 at 17:28
Here is a good example: Let $k$ be a field and consider the field of formal power series $\sum_{i \in I} a_i t^i$ where $I$ can be any well-ordered subset of $\mathbb{R}$. Sum and product are defined formally by $\sum (a_i+b_i) t^i$ and $\sum a_i b_j t^{i+j}$. Exercise: The sum or product of two formal power series of this form is another one, and every coefficient of the sum or product is a finite polynomial in the coefficents of the summands/multiplicands. The valuation is $v(\sum a_i t^i) = \min(i : a_i \neq 0)$. – David Speyer Feb 2 '11 at 18:10

I suggest having a look to Bosch, Güntze and Remmert's "Non-archimedean analysis: a systematic approach to rigid analytic geometry" (1984)

They cover quite a lot of things about valuations and norms.

share|cite|improve this answer

Take any valuation ring, which is not noetherian.

share|cite|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.