• Title, Summary, Keyword: w-copure flat module

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  • Bouba, El Mehdi;Kim, Hwankoo;Tamekkante, Mohammed
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.3
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    • pp.763-780
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    • 2020
  • 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.