Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

Is there any easy nice example to say that this element of $k((t))$ is transcendental over $k(t)$ (We can use the cardinality argument for the existence of transcendental element.But, I am looking example). Thank you

share|cite|improve this question
$k((t))$ denotes formal power series? What about $\phi=\prod_n \frac1{1-t^n}$? It has infinitely many "poles" in $\bar k$, hence in any polynomial with coefficients in $k(t)$ there is some pole $z$ not occuring as pole or zero of any coefficient. Therefore $z$ is also a pole of order $\deg p$ of $p(\phi)$. – Hagen von Eitzen Sep 16 '12 at 15:17

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.