Extension of i-Modularity

Abstract

Let k be a field of characteristic p ≠ 0. The main purpose of this paper is to extend the results and definitions of i-modularity that have already been estalished by Chellali and the present author when [k : kp] is finite to the case of finite irrationality degree extensions. A number of properties of i-modular extensions are determined and examples are presented illustrating the results. In particular, we characterize some special cases.