On?w-copure flat modules and dimension

摘要

Let?R?be a commutative ring. An?R-module?M?is said to be?w-flat if?Undefined control sequence Tor?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.