[理工] [離散] atom & ring

[taitin (小南)]

1.Suppose that (K,．,+)is a Boolean algeba
  and a is an atom of K.
  Prove that a．b=0 or a．b=a for every a,bεK

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


這兩題困擾我很久~請高手解答~謝謝

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推 polomoss:台大98期中考~待會回你
推 polomoss:別人寫的第一題:假設 a 為 atom, 利用矛盾證法,
→ polomoss:若存在一 b 使得 a*b=0 or a*b=a => 0<c 且 c<a, →←
→ polomoss:其實我有點看不懂XD
→ fscnick:(K,+,‧)跟(K,‧,+)有一樣嗎?
推 crazyjoe:一樣
→ fscnick:假設 a*b=c 且c=/=0,c=/=a => c<a => a 不為atom
→ fscnick:反證法  不知道這樣對不對...