Let f : R → S and g : S → T be ring homomorphisms.
(a) Prove that g ◦ f : R → T is also a ring homomorphism.
(b) If f and g are isomorphisms, prove that g ◦ f is also an
isomorphism.
a.) Write down the formulas for all homomorphisms from Z10 into
Z25.
b.)Write down the formulas for all homomorphisms from Z24 into
Z18.
c.)Write down the formulas for all homomorphisms from Z into
Z10.
d.)Extra: Define φ : C x → Rx by φ(a + bi) = a 2 + b 2 for all a
+ bi ∈ C x where R is the real numbers and C is the complex
numbers. Show that φ is a homomorphism.