作者hotplushot (热加热)
看板Math
标题[代数] 几题代数
时间Thu Jun 23 17:04:32 2011
1.find a finite ring with characteristic 4.
2.find a infinite ring with characteristic 4.
3.
f:R→S is a homo of rings with identity
and u is a unit in R such that f(u) is a unit in S,
then f(1_R)=1_S and f(u^-1)=f(u)^-1
4.
|G|=(p^n)q, with p>q(p, q are primes), then G contians a unique normal
subgroup of index q.
5.找一个环(包含identity u) 其子环的identiy不为u.
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 111.252.193.181
1F：→ lockheart :3.f(1_R)=f((1_R)^2)=f(1_R)^2. Since 1_R is a unit 06/23 18:32
2F：→ lockheart :in R, f(1_R) is a unit in S. By cancellation law 06/23 18:33
3F：→ lockheart :we can find that f(1_R)=1_S. Moreover 1_S=f(1_R) 06/23 18:35
4F：→ lockheart :=f(u*u^-1)=f(u)*f(u^-1) for some unit u in R, 06/23 18:36
5F：→ lockheart :f(u^-1)=f(u)^-1. 06/23 18:37
6F：→ lockheart :4. R_1*R_2 and {0}*R_2 06/23 18:44
感谢!!!
※ 编辑: hotplushot 来自: 111.252.193.181 (06/23 19:53)
7F：→ Vulpix :4. Sylow's Thm. 06/23 21:07
8F：→ Vulpix :1. Z/(4) 2. 无限多个Z/(4)直积 06/23 21:10
9F：→ RoamingGhost:or any polynomial ring over Z/4Z, like Z/4Z [t] 06/24 00:35