The problem is to prove that the existence of an idempotent (an element whose "square" is itself, that isb*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 supposea*a=a, whereaES. Assumef: <S,*> --> <T,#> is an isomorphism. Thenx=f(a)ET. Now,

x#x =f(a) #f(a) by substitution

=f(a*a) by operation preserving

=f(a) sincea*a=a

=xas desired.

Hence, the existence of an idempotent is a srtuctural property.