On P-Hv-modules, their isomorphism theorems and their fundamental relations

Abstract

In this paper, we study a wide class of [Formula: see text]-modules obtained from ordinary [Formula: see text]-modules by using [Formula: see text]-hyperoperations. We define a new [Formula: see text]-[Formula: see text]-module over [Formula: see text]-[Formula: see text]-rings and study several properties of it starting from the isomorphism theorem to the fundamental relation.