0
votes
2answers
33 views

Subgroups which are not subspaces

Let $p$ be a prime number. Is every subgroup of the abelian group $\Bbb Z_p^2$ a subspace of it as a vector space over $\Bbb Z_p$? Can it be generalized to all finite fields?
4
votes
3answers
176 views

Embedding torsion-free abelian groups into $\mathbb Q^n$?

Glass' Partially Ordered Groups states without proof: Every torsion-free abelian group can be embedded into a rational vector space (as a group). Can someone link me to a proof of this? It ...
5
votes
1answer
265 views

Adjoint of forgetful functor between category of vector spaces and category of abelian groups

I've just found out about the forgetful functor between the category of vector spaces and the category of abelian groups. It maps a vector space to it's additive abelian group. My question is, is ...
6
votes
3answers
265 views

Is $\mathbb{Z}(p^{\infty})$ a vector space over some field $\mathbb{F}$?

I don't know how to write in good English, so I will follow Hungerford's word from his book Algebra. The following relation on the additive group $\mathbb{Q}$ of rational numbers is a congruence ...