• 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)
  • Received : 2019.05.16
  • Accepted : 2019.09.05
  • Published : 2020.05.31


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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