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# Science Fair Project Encyclopedia

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# Algebra homomorphism

A homomorphism between two algebras over a field K, A and B, is a map $F:A\rightarrow B$ such that for all k in K and x,y in A,

• F(kx)=kF(x)
• F(x+y)=F(x)+F(y)
• F(xy)=F(x)F(y)
Last updated: 08-02-2005 14:47:11
03-10-2013 05:06:04