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

Answer 1

What is a uniform group?

Answer 2

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

Answer 3

lol what is indecomposable?

Answer 4

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

Answer 5

A is not decomposable is called indecomposable. :)