let k be a field with charkp0 show that in the field kx of rational functions over k the element

Name: let k be a field with charkp0 show that in the field kx of rational functions over k the element x has no pth root 92515
Uploaded: 2023-08-21T13:33:32-08:00
Duration: 2 min 39 s
Channel: Sri K
Description: let k be a field with charkp0 show that in the field kx of rational functions over k the element x has no pth root 92515

Question

Vikash Ranjan · Accepted Answer

1. Suppose there exists a rational function f(x) in K(x) such that (f(x))^p = x.

Question

Let K be a field with char(K)=p>0. Show that in the field K(x) of rational functions over K, the element x has no p^th root.

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