作者hanabiz (再见 B67)
看板Math
标题Re: [代数] 习题几问
时间Tue Jan 4 23:48:35 2011
应推文稍微简介一下characteristic (顺便复习XD)
let R(=\={0}) be a ring with unit e
let a属於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属於 N联集{0}
suppose that k =\= 0 => kx=0, for all x 属於 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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1F：→ hanabiz :有打错或哪边太简略看不懂请推文 01/04 23:50
2F：推 jacky7987 :喔喔感谢学长﹨(╯▽╰)∕ 01/04 23:51
3F：→ jacky7987 :所以(a+b)^p≡a^p+b^p只有在char(R)是p的时候才会对 01/04 23:52
4F：→ jacky7987 :是吗? 01/04 23:52