I encountered this sentence, but I could not understand it.

The direct sum of free modules is free. Take the union of the basis elements over each component to build a basis for M. But the converse is not true.Z6 is the direct sum ofZ2 andZ3, yet the two summands are not freeZ6 modules.

Zn (Z subscript n) denotes the set of integers modulo n.

What are the examples of freeZ6 modules?

WhyZ2 andZ3 cannot be freeZ6 modules?

Thanks in advance.