Category of n-weak injective and n-weak flat modules with respect to special super presented 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 $\mathcal{W}{\mathcal{I}}_k^n(R)$ and $\mathcal{W}{\mathcal{F}}_k^n(R^{op})$ which are larger than that of modules with weak injective and weak flat dimensions at most k. Then over any arbitrary ring, we study the existence of $\mathcal{W}{\mathcal{I}}_k^n(R)$ and $\mathcal{W}{\mathcal{F}}_k^n(R^{op})$ covers and pre-envelopes.

Keywords:

• n-super finitely presented
• n-weak flat-cover
• n-weak flat-envelope
• n-weak flat module
• n-weak injective module

2020 Mathematics Subject Classification:

• 16D80
• 16E05
• 16E30
• 16E65
• 16P70

Acknowledgments

The authors would like to thank the referee for the helpful suggestions and valuable comments.