[代數] homomorphism

看板Math作者 (無法顯示)時間14年前 (2011/07/15 10:34), 編輯推噓1(1推 0噓 2→)
留言3則, 1人參與, 最新討論串2/4 (看更多)
(1) if f:(R,+.*) -> (S,⊕,⊙) is a ring homomorphism and onto, where |S|>1 show that if R is commutative, then S is commutative (2) suppose that f: G->H is a group homomorphism and f is onto prove that if G is a abelian, then H is abelian 請問這兩題應該怎麼證呢? 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 218.166.118.147
推
07/15 13:00, , 1F
1. Given s_1 s_2 in S. Since f is onto
07/15 13:00, 1F
→
07/15 13:01, , 2F
there exist r_1 r_2 such that f(r_i)=s_i,i=1,2
07/15 13:01, 2F
→
07/15 13:01, , 3F
第二題也差不多!?
07/15 13:01, 3F
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文章代碼(AID): #1E7wSj71 (Math)
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文章代碼(AID): #1E7wSj71 (Math)