Regularity criteria for semianalytic algebra of prime characteristic

Let S be a semianalytic algebra over a field k of characteristic p > 0 and S p the local ring with respect to p ∈ Spec ( S ) . In this article, for a semianalytic algebra we introduce the concept of semianalytic p n -basis which generalizes the p n -basis defined in [1] , and the concept of a p n -admissible field for a semianalytic field extension, we give regularity criteria for the ring S p without reducibility assumption. The results are extension of our previous results for affine algebra to the case of semianalytic algebra (cf. [1] ), and these are generalization of results of Orbanz [6] in the semianalytic case of prime characteristic.