** Let be a homomorphism of Abelian groups. Show that for each .**

Proof:

Since f is a homomorphism, and since , an Abelian group, then:

(by associativity)

(f is a homomorphism)

The last line is true because (but that’s another proof).

Advertisements

Filed under: Algebra, Proof of the Day | Tagged: abelian, associative, commutative, group, homomorphism | Leave a comment »