Work

On τq-flatness and τq-coherence

Year: 2024

Type: article

Abstract: In this paper, we first introduce and study the notions of [Formula: see text]-flat modules. Then study the rings over which all modules are [Formula: see text]-flat (which is called [Formula: see text]-VN regular rings). In particular, we show that a ring [Formula: see text] is a [Formula: see text]-VN regular ring if and only if T[Formula: see text] is a von Neumann regular ring, if and only if [Formula: see text] is a reduced ring with Min[Formula: see text] compact. Finally, we obtain the Chase theorem for [Formula: see text]-coheret rings: a ring [Formula: see text] is [Formula: see text]-coherent if and only if any direct product of [Formula: see text] is [Formula: see text]-flat if and only if any direct product of flat [Formula: see text]-modules is [Formula: see text]-flat. Some examples are provided to compare with the known conceptions.

Source: Journal of Algebra and Its Applications

DOI: 10.1142/s0219498826500106

Authors: Xiaolei Zhang, Wei Qi

Institutions: Shandong University of Technology, Tianshui Normal University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G2960538719, G4280471265