All rings are with unity but not necessarily commutative.
We know that if a ring $R$ is left semisimple (a direct sum of minimal left ideals), then it is left artinian.
My question is: if an unital $R$-module $_R M$ is semisimple (a direct sum of simple $R$-submodule of $_R M$), is $_R M$ left artinian?
No, there is no direct relationship: you can take any simple module $S$ and then $\oplus_{i\in \mathbb N} S$ is semisimple but not Artinian.
Over a field every module is semisimple, but the only Artinian ones are the finitely generated ones.