On p-semilinear transformations

In this paper, we introduce pp-semilinear transformations for linear algebras over a field bfFbfF of positive characteristic pp, discuss initially the elementary properties of pp-semilinear transformations, make use of it to give some characterizations of linear algebras over a field bfFbfF of positive characteristic pp. Moreover, we find a one-to-one correspondence between pp-semilinear transformations and matrices, and we prove a result which is closely related to the well-known Jordan-Chevalley decomposition of an element.