Absolutely MI-pure Modules And Relative MI-injeetive And MI-Flat Modules

In this article, we mainly study two aspects:In the first part, we first define absolutely Fl-pure modules and prove that the absolutely FI-pure modules are equivalent with absolutely E- pure modules, which provides new characterizations of absolutely E-pure modules; then we introduce the concept of absolutely MI-pure modules and their properties.In the second part, we define n-MI-injective and n-MI-flat modules based on MI-injective and MI-flat modules, and study their properties and some equiva-lence conditions under max-coherent ring; Finally, we give the related properties and conclusion about max-n-injective and max-n-flat modules.