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
Transcendental extension
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abstract-algebra
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2$k((t))$ 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 $p(\phi)$. – 2012-09-16