Galois corings and a Jacobson–Bourbaki type correspondence

The Jacobson–Bourbaki Theorem for division rings was formulated in terms of corings by Sweedler in [M.E. Sweedler, The predual theorem to the Jacobson–Bourbaki Theorem, Trans. Amer. Math. Soc. 213 (1975) 391-406]. Finiteness conditions hypotheses are not required in this new approach. In this paper we extend Sweedler's result to simple artinian rings using a particular class of corings, comatrix corings. A Jacobson–Bourbaki like correspondence for simple artinian rings is then obtained by duality.