I have in my notes that the Jacobson radical of a ring $R$ is: 
$J(R) = \cap${$I$ | $I$ primitive ideal of $R$}
$= \cap$ {$Ann\_R M$ | $M$ simple $R$-module}.

I have now seen elsewhere that
$J(R) = \{x ∈ R: xy-1 ∈ R^\times \text{ for all } y ∈R\}$

I was just wondering would anyone be able to provide an explanation as to how to get from one definition to the other? Thanks.