An explicit version of the correspondence between Noetherian modules with Cartier maps and Artinian modules with Frobenius maps

In this paper, we introduce an explicit version of the correspondence between Noetherian modules with Cartier maps and Artinian modules with Frobenius maps which recovers the correspondence given by R. Y. Sharp and Y. Yoshino, and the correspondence given by M. Blickle and G. Böckle. ***************************************************************************************************************** *****************************************************************************************************************