Answer to Question #16886 in Abstract Algebra for Mohammad
Is Z12 semisimple Z-module?
Z_12=Z_3 +Z_4 Z_3 is simple Z-module but 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