On w-copure flat modules and dimension
Bull. Korean Math. Soc.
Published online October 16, 2019
El Mehdi Bouba, Hwankoo Kim, and Mohammed Tamekkante
University Moulay Ismail Meknes, Hoseo University
Abstract : Let R be a commutative ring. An R-module M is said to be w-flat if Tor^R_1(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 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.
Keywords : w-copure flat module, strongly w-copure flat module, w-copure flat dimension
MSC numbers : 13D05, 13D07, 13H05
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