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Apr 13, 2022 at 20:03 comment added Sam Hopkins Yes. I guess I just meant that since the (false) assertion is "weaker" with field instead of ring, as a false belief it might be more common.
Apr 13, 2022 at 20:03 history edited Or Shahar CC BY-SA 4.0
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Apr 13, 2022 at 20:02 comment added Or Shahar @SamHopkins Well, if $R=\Bbb{F}_p$ then $x^p$ is an automorphism because it’s a 1 to 1 on a finite set and endomorphism. If the field is infinite, then take $\Bbb{F}_p(x)$, there isn’t exist $f(x)\in \Bbb{F}_p(x)$ such that $f(x)^p=x$
Apr 13, 2022 at 19:47 comment added Sam Hopkins But even with field it is still false?
Apr 13, 2022 at 19:45 comment added Or Shahar @SamHopkins Pay attention, I changed the statement because accidentally I wrote field instead of ring
Apr 13, 2022 at 19:44 history edited Or Shahar CC BY-SA 4.0
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S Apr 13, 2022 at 17:57 history answered Or Shahar CC BY-SA 4.0
S Apr 13, 2022 at 17:57 history made wiki Post Made Community Wiki by Or Shahar