φ-平坦余挠理论

doi:10.16088/j.issn.1001-6600.2019082802

Abstract

Abstract: In this paper, the φ-flat cotorsion theory which is showed to be a perfect cotorsion theory is introduced and studied. Assume R is a φ-ring. It is proved that the φ-flat cotorsion theory coincides with the classical flat cotorsion theory if and only if R is a domain. As an application, new characterizations of Nonnil-coherent rings and φ-von Neumann rings are given. Finally, the envelope property of φ-flat modules is investigated and showing that every R-module has a surjective (pre)envelope if and only if R is a Nonnil-coherent ring and all φ-flat R-modules are closed under submodules.

Key words: cotorsion theory, covering class, enveloping class, φ-flat module, φ-cotorsion module

CLC Number:

O154.2

ZHANG Xiaolei, ZHAO Wei, WANG Fanggui. On φ-flat Cotorsion Theory[J].Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(2): 119-124.

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On φ-flat Cotorsion Theory

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