On [formula omitted]p-extensions of commutative rings

Abstract

We study Z p -extensions of a commutative ring R. Some general properties corresponding to the finite Galois theory by Chase, Harrison and Rosenberg are proved. After that, we consider Z p -extensions of commutative rings of characteristic p. We describe the structure of a Z p -extension and the Z p -module T( Z p , R) of the isomorphism classes of Z p -extensions of R, via Witt vectors. Results on cyclic p n -extensions of rings of characteristic p, which are already known, are also recovered by direct and elementary methods.