Regularity criteria for semianalytic algebra of prime characteristic

Let S be a semianalytic algebra over a field k of characteristic p>0 and Sp the local ring with respect to p∈Spec(S). In this article, for a semianalytic algebra we introduce the concept of semianalytic pn-basis which generalizes the pn-basis defined in [1], and the concept of a pn-admissible field for a semianalytic field extension, we give regularity criteria for the ring Sp 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.