Rings with finite n-Weak injective dimension and (n,k)-Weak cotorsion modules

TL;DR

This paper introduces and studies (n,k)-weak cotorsion modules over rings, extending existing notions, and explores their properties, examples, and applications in module theory.

Contribution

It defines (n,k)-weak cotorsion modules based on n-weak flat dimensions and investigates their properties and applications, extending prior concepts in module theory.

Findings

Defined (n,k)-weak cotorsion modules and their properties

Provided examples illustrating the new concepts

Explored applications in module theory

Abstract

Let R be a ring and n,k be two non-negative integers. As an extension of several known notions, we introduce and study (n,k)-weak cotorsion modules using the class of right R-modules with n-weak flat dimensions at most k. Various examples and applications are also given.