대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제61권1호
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  • Pages.1-12
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  • 2024
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A COTORSION PAIR INDUCED BY THE CLASS OF GORENSTEIN (m, n)-FLAT MODULES

  • Qiang Yang (Institute for Advanced Study in History of Science Northwest University)
  • 투고 : 2022.08.21
  • 심사 : 2023.11.27
  • 발행 : 2024.01.31
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초록

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 (𝓖𝓕m,n(R),𝓖𝓒m,n(R)) constitutes a hereditary perfect cotorsion pair (where 𝓖𝓕m,n(R) denotes the class of Gorenstein (m, n)-flat modules and 𝓖𝓒m,n(R) refers to the class of Gorenstein (m, n)-cotorsion modules) over slightly (m, n)-coherent rings.

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참고문헌

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