(a) For any abelian group A and positive integer m, Hom(Z_m,A) ≅ A[m] = {a ϵ A| ma = 0}

(b) Hom(Z_m,Z_n) ≅ Z_(m,n)•

(c) The Z-module Z_m has Z_m * = 0.

(d) For each k ≥ 1, Z_m is a Z_mk•module (Exercise 1.1); as a Z_mk·module,Z_m * ≅ Z_m.

Data from exercise 1.1

If R has an identity and P is a finitely generated projective unitary left R-module, then (a) P* is a finitely generated projective right R-module. (b) P is reflexive. This proposition may be false if the words "finitely generated" are omitted;