[代數] subring相關的問題

看板Math作者 ( )時間11年前 (2012/12/09 23:44), 編輯推噓2(2推 0噓 6→)
留言8則, 2人參與, 最新討論串1/2 (看更多)
(R, +, ·) is a ring, S is a finite nonempty subset of R (S, +, ·) is a subring of R if for a,b in S, a+b in S and a·b in S 請問這應該要怎麼證明? -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 114.25.194.32
推
12/09 23:55, , 1F
這是101台大資工離散考題吧..?
12/09 23:55, 1F
→
12/09 23:56, , 2F
S是有限ring 先證出for all a, -a屬於S
12/09 23:56, 2F
→
12/09 23:57, , 3F
記錯了 應該是97年的才對
12/09 23:57, 3F
→
12/09 23:59, , 4F
恩 可是我想不出來要怎麼從finite導到-a in S
12/09 23:59, 4F
推
12/10 00:01, , 5F
S={s1,s2,..sn}, for all a in S, {a+s1, a+s2,..}
12/10 00:01, 5F
→
12/10 00:02, , 6F
{a+s1, a+s2,.., a+sn}=S={s1,s2,..sn}
12/10 00:02, 6F
→
12/10 00:03, , 7F
a=a+sk=sk+a, for some k, 得sk為zero in S
12/10 00:03, 7F
→
12/10 00:04, , 8F
zero = a+st = st+a, for some t, 得-a=st in S
12/10 00:04, 8F
‣ 更多 lachu 的文章
文章代碼(AID): #1GnB7FVW (Math)
‣ 更多 lachu 的文章
文章代碼(AID): #1GnB7FVW (Math)