대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제57권3호
  • /
  • Pages.763-780
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  • 2020
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON w-COPURE FLAT MODULES AND DIMENSION

  • Bouba, El Mehdi (Department of Mathematics Faculty of Science University Moulay Ismail Meknes) ;
  • Kim, Hwankoo (Division of Computer & Information Engineering Hoseo University) ;
  • Tamekkante, Mohammed (Department of Mathematics Faculty of Science University Moulay Ismail Meknes)
  • 투고 : 2019.05.16
  • 심사 : 2019.09.05
  • 발행 : 2020.05.31
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⟨ 이전 논문 다음 논문 ⟩

초록

Let R be a commutative ring. An R-module M is said to be w-flat if Tor R1 (M, N) is GV -torsion for any R-module N. It is known that every flat module is w-flat, but the converse is not true in general. The w-flat dimension of a module is defined in terms of w-flat resolutions. In this paper, we study the w-flat dimension of an injective w-module. To do so, we introduce and study the so-called w-copure (resp., strongly w-copure) flat modules and the w-copure flat dimensions for modules and rings. The relations between the introduced dimensions and other (classical) homological dimensions are discussed. We also study change of rings theorems for the w-copure flat dimension in various contexts. Finally some illustrative examples regarding the introduced concepts are given.

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과제정보

The authors would like to express their gratitude to an anonymous reviewer of this paper for his insightful comments and suggestions which have greatly improved the paper. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A3B03033342).

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