K^p=K Meaning: Field Characteristic p

  • Thread starter Thread starter futurebird
  • Start date Start date
  • Tags Tags
    Notation
futurebird
Messages
270
Reaction score
0
K is a field and it has characteristic p \neq 0. What is the meaning of K^{p}=K -- ?
 
Physics news on Phys.org
K^p = { k^p : k in K }. So K^p = K means that every element in K has a pth root.
 
Thanks!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Prove: Limit Point of H ∪ K if p is Limit Point of H or K
Replies
5
Views
2K
Show that k is an odd integer, except when k=2
Replies
9
Views
2K
Show that x -> x^p is an automorphism in K
Replies
14
Views
2K
Value of p for dp/dt to be maximum
Replies
25
Views
2K
Eisenstein's criterion proof
Replies
13
Views
2K
Given that p is a prime? (Review/verify this proof)?
Replies
4
Views
1K
Repeated root in field of char 0
Replies
12
Views
2K
Computing conditional extinction probabilities for pollen cells
Replies
1
Views
1K
Prove that ## 1^{p}+2^{p}+3^{p}+\dotsb +(p-1)^{p}\equiv 0\pmod {p} ##.
Replies
6
Views
3K
Understanding Scattering Process in QFT Integral
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top