Question

Is Z_4 semisimple Z-module?

Answer 1

Z_4 is not semisimple. because it cant be split to the direct sum of simple
Z-modules. Why? because all simple Z-modules looks like Z_p where p is prime. so
for Z_4 we have only 1 possibility Z_4=Z_2 + Z_2. but its not true
so Z_4 is
not semisimple