[代數] 幾題代數

看板Math作者 (熱加熱)時間14年前 (2011/06/23 17:04), 編輯推噓0(0推 0噓 9→)
留言9則, 3人參與, 最新討論串6/7 (看更多)
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.找一個環(包含identity u) 其子環的identiy不為u. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 111.252.193.181
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06/23 18:32, , 1F
3.f(1_R)=f((1_R)^2)=f(1_R)^2. Since 1_R is a unit
06/23 18:32, 1F
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06/23 18:33, , 2F
in R, f(1_R) is a unit in S. By cancellation law
06/23 18:33, 2F
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06/23 18:35, , 3F
we can find that f(1_R)=1_S. Moreover 1_S=f(1_R)
06/23 18:35, 3F
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06/23 18:36, , 4F
=f(u*u^-1)=f(u)*f(u^-1) for some unit u in R,
06/23 18:36, 4F
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06/23 18:37, , 5F
f(u^-1)=f(u)^-1.
06/23 18:37, 5F
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06/23 18:44, , 6F
4. R_1*R_2 and {0}*R_2
06/23 18:44, 6F
感謝!!! ※ 編輯: hotplushot 來自: 111.252.193.181 (06/23 19:53)
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06/23 21:07, , 7F
4. Sylow's Thm.
06/23 21:07, 7F
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06/23 21:10, , 8F
1. Z/(4) 2. 無限多個Z/(4)直積
06/23 21:10, 8F
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06/24 00:35, , 9F
or any polynomial ring over Z/4Z, like Z/4Z [t]
06/24 00:35, 9F
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文章代碼(AID): #1E0m6Zez (Math)
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文章代碼(AID): #1E0m6Zez (Math)