hntroduction. In 1944, Jacobson [4] developed a Galois theory for nonnormal and nonseparable fields; and, in 1949, Hochschild [3] used the techniques of Jacobson to present a Galois theory for division rings. These same techniques will be used in this paper to present a Galois theory for rings with identity element. The theory presented here is the analogue of the outer Galois theory for division rings and it extends the Galois theory of commutative rings developed by Chase, Harrison, and Rosenberg [1].