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Math Help - Proof-Abstract Algebra

  1. #1
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    Proof-Abstract Algebra

    The problem is to prove that the existence of an idempotent (an element whose "square" is itself, that is b * b = b) is a structural property.

    I would just like someone to proofread my proof and give me some feedback....Thanx! (note: E="an element of")

    Pf: Let <S,*> and <T,#> be isomorphic algebraic structures and suppose a*a=a, where a E S. Assume f: <S,*> --> <T,#> is an isomorphism. Then x=f(a) E T. Now,

    x#x = f(a) # f(a) by substitution
    = f(a*a) by operation preserving
    = f(a) since a*a=a
    = x as desired.
    Hence, the existence of an idempotent is a srtuctural property.
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  2. #2
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    I feel confident that my proof is OK...but is there anyone that can proofread this and give me any feedback? Any comments are welcome and I take constructive criticizm very well; that's how I learn.
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