2.Suppose that(R,+,．)and(S,⊕,⊙) are two rings
with zero element Zr and Zs respectively.
Given a ring homorphism f:R→S,let K={aεR|f(a)=Zs}
Prove that
(a)(K,．,+) is a ring
(b)K is an ideal of R
謝謝
Research Space for Linear Algebra & Discrete Mathematics
5 則留言:
(a) 證 (K,+,．) 為 (R,+,．) 之 subring: ∀ a,b∈K,
(i) f(a-b)=f(a)-f(b)=0∈K
(ii) ∀ a,b∈K, f(ab)=f(a)⊙f(b)=0∈K
所以 (K,+,．) 為 ring
(b) ∀ a∈K, b∈R, 因為 f(ab)=f(ba)=0,
所以 K is an ideal of R
謝謝助教
(i) f(a-b)=f(a)-f(b)=0∈K
^^^
這邊的 - 是不是要有圈圈，因為是右邊的運算
Prove that
(a)(K,．,+) is a ring
(b)K is an ideal of R
題目問"(K,．,+)" 乘法和加法是題目有打錯嗎?不然應該連"(K,．,+)" 都不是環了吧@@
Tse: 是的, 我想你應該知道所以我就懶的打了
pai: 他應該只是放反了
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