Category of n-weak injective and n-weak flat modules with respect to special super presented modules

TL;DR

This paper introduces and characterizes n-weak injective and n-weak flat modules using special super finitely presented modules, exploring their properties and existence of covers and preenvelopes over arbitrary rings.

Contribution

It defines new classes of modules, provides characterizations via special super finitely presented modules, and studies the existence of covers and preenvelopes for these classes.

Findings

Characterization of n-weak injective and n-weak flat modules.

Introduction of larger classes $\\mathcal{WI}_k^n(R)$ and $\mathcal{WF}_k^n(R^{op})$.

Existence results for covers and preenvelopes of these modules.

Abstract

Let $R$ be a ring and $n$, $k$ two non-negative integers. In this paper, we introduce the concepts of $n$-weak injective and $n$-weak flat modules and via the notion of special super finitely presented modules, we obtain some characterizations of these modules. We also investigate two classes of modules with richer contents, namely $\mathcal{WI}_k^n(R)$ and $\mathcal{WF}_k^n(R^{op})$ which are larger than that of modules with weak injective and weak flat dimensions less than or equal to $k$. Then on any arbitrary ring, we study the existence of $\mathcal{WI}_k^n(R)$ and $\mathcal{WF}_k^n(R^{op})$ covers and preenvelopes