On Zp-extensions of commutative rings

AbstractWe study Zp-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 Zp-extensions of commutative rings of characteristic p. We describe the structure of a Zp-extension and the Zp-module T(Zp, R) of the isomorphism classes of Zp-extensions of R, via Witt vectors. Results on cyclic pn-extensions of rings of characteristic p, which are already known, are also recovered by direct and elementary methods