Let $R$ be a semisimple ring with a finite number of left maximal ideals. (Here "semisimple" means that the Jacobson radical is zero.)
Show that $R \cong R_1 \times ... \times R_n$
Such that every $R_i$ is a division ring or $R_i \cong M_{n_i}(K_i)$ for a finite field $K_i$
I'm completely stuck. any help will be appreciated.