[代數] Characteristic
我們知道一個field的characteristic不是定義為0就是一個prime
想請問一下
if Char(F) = p =/= 0
then Char(F[a]) =?= p
a€K is an extension field of F
where F[a]={f(a)│f(x)€F[x]} (F adjoining a)
有同學是說
if Char(F) = p =/= 0
then for all b€F[a] , b = 1*b , 1同時是F與F[a]的元素
所以 p*b = p*(1*b) = (p*1)*b = 0*b = 0 (因為1€F , 所以p*1=0)
但是p*b的意思不是說 b加p次嗎
p個b
= b + b +....+ b
= 1*b + 1*b +....+1*b
= p個1*b
怎麼可以p跟1先作用？
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