Prove that a nonzero additive abelian group is uniform if and only if the intersection of any two nonzero subgroups must also be nonzero.
Please, help @zzr0ck3r

Question

Prove that a nonzero additive abelian group is uniform if and only if the intersection of any two nonzero subgroups must also be nonzero.
Please, help @zzr0ck3r

zzr0ck3r · Answer

What is a uniform group?

loser66 · Answer

A is called uniform provided every nonzero subgroup of A is indecomposable.

zzr0ck3r · Answer

lol what is indecomposable?

loser66 · Answer

A is decomposable provided there exist groups B and C, both nonzero, such that $A\cong B\times C$

loser66 · Answer

A is not decomposable is called indecomposable. :)