→ hanabiz :有打錯或哪邊太簡略看不懂請推文 01/04 23:50
推 jacky7987 :喔喔感謝學長﹨(╯▽╰)∕ 01/04 23:51
→ jacky7987 :所以(a+b)^p≡a^p+b^p只有在char(R)是p的時候才會對 01/04 23:52
→ jacky7987 :是嗎? 01/04 23:52
應推文稍微簡介一下characteristic (順便複習XD)
let R(=\={0}) be a ring with unit e
let a屬於R => f:Z->R is a ring-homo
f(1)=e
f(n)=na
ker(f) is an ideal of Z and in fact, ker(f) = kZ for some k屬於 N聯集{0}
suppose that k =\= 0 => kx=0, for all x 屬於 R
we say that R has characteristic k
<ex> f:Z->Z
f(1)=1
f(n)=n
=>ker(f)=0
we say that Z has characteristic 0
Q: what is the characteristic of Q ?
A: f:Z->Q
f(1)=1
f(n)=n
=>ker(f) = 0
Q: what is the characteristic of Z/5Z ?
A: f:Z->Z/5Z
f(1)=1(mod 5)
f(n)=n(mod 5)
=>ker(f) = 5Z
Z/5Z has characteristic 5
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