Hi:

Suppose that $\displaystyle R$ is an arbitrary simple ring such that $\displaystyle R^2 notequal (0)$ and such that $\displaystyle R$ contains a maximal right ideal $\displaystyle A$ (which is certainly the case if $\displaystyle R$ has a unity). Up to here the statement. Now, why does $\displaystyle R$ contain a maximal right ideal if it has a unity? I don't get this. Thanks.