In [2], M. Auslander and O. Goldman introduced the notion of Galois extension of commutative rings. Recently, in [5], S. U. Chase, D. K. Harrison and A. Rosenberg gave a generalization of the fundamental theorem of Galois theory. In the first section of this note, we shall extend to a case of noncommutative rings the definition of Galois extension which is defined by Chase, Harrison and Rosenberg in the case of commutative rings. Then we shall establish a half of the fundamental theorem of

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... s theory by the method that is completely similar to the method used by Chase, Harrison and Rosenberg. In the second section, we shall study on a Galois extension over commutative rings and we shall show that if a ring Γ is an inner Galois extension of its center C, then Γ is generated by units of Γ over C.