Let $(G,+)$ be an abelian group. Does there always exist a ring with unity $(R,+,\cdot)$ and an injective homomorphism of groups $ \psi:G\rightarrow R$?

Is this hard to prove, or are there simple proofs?

Let $(G,0,+)$ be an abelian group. Does there always exist a ring with unity $(R,0,1,+,\cdot)$ and an injective homomorphism of groups $ \psi:(G,0,+)\rightarrow (R,0,+)$?

Is this hard to prove, or are there simple proofs?

Let $(G,+)$ be an abelian ring. Always exists a ring with unity $(R,+,\cdot)$ and an injective homomorphism of groups $ \psi:G\rightarrow R$.

Is this hard to prove, or are simple proofs?

Let $(G,+)$ be an abelian group. Does there always exist a ring with unity $(R,+,\cdot)$ and an injective homomorphism of groups $ \psi:G\rightarrow R$?

Is this hard to prove, or are there simple proofs?