Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2024; 61(1): 1-12

Online first article January 16, 2024      Printed January 31, 2024

https://doi.org/10.4134/BKMS.b220580

Copyright © The Korean Mathematical Society.

A cotorsion pair induced by the class of Gorenstein $(m,n)$-flat modules

Qiang Yang

Northwest University

Abstract

In this paper, we introduce the notion of Gorenstein $(m,n)$-flat modules as an extension of $(m,n)$-flat left $R$-modules over a ring $R$, where $m$ and $n$ are two fixed positive integers. We demonstrate that the class of all Gorenstein $(m,n)$-flat modules forms a Kaplansky class and establish that ($\mathcal{GF}_{m,n}(R)$,$\mathcal{GC}_{m,n}(R)$) constitutes a hereditary perfect cotorsion pair (where $\mathcal{GF}_{m,n}(R)$ denotes the class of Gorenstein $(m,n)$-flat modules and $\mathcal{GC}_{m,n}(R)$ refers to the class of Gorenstein $(m,n)$-cotorsion modules) over slightly $(m,n)$-coherent rings.

Keywords: Slightly $(m,n)$-coherent ring, $(m,n)$-flat module, Gorenstein $(m,n)$-flat modules, cotorsion pair, Kaplansky class

MSC numbers: Primary 13D05, 13H10, 16E30