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We know that all finite fields are perfect (fields with char $p$). Also fields with char 0 (infinite fields) are perfect. Then what are the fields that are not perfect?

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    By your remarks, it has to be an infinite field of characteristic $p$. The first such thing that comes to mind, $\mathbb{F}_p(T)$, turns out to work (why?).2012-02-07
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    sorry, I want to ask an example of a field that is not perfect.- Madhav Bapat2012-02-07
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    (You can edit your post to reflect your comment).2012-02-07
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    To Cam McLeman,Thanks for suggestion- Bapat2012-02-07
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    May I ask you to post an answer to your own question? In such a way you will be sure that your intuition is correct and the question will not remain in the "unanswered" category forever! If you don´t have time to do that just let it know to someone who can answer. Thank you and welcome to Math.Se!2012-02-07

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