Ⅰ-flat Modules

Let R be a commutative Noetherian ring, I an ideal of R such thatht(â… )＞0.In the chapter two, we will recall some basic concepts and propertiesin commutative algebra and homological algebra. In the chapter three,wewill defineâ… -flat modules and give equivalent conditions: one module M isanâ… -flat R-module if and only if for all prime ideals p,Supp(Tor₁^R(M, R/p))(?)V(â… ). And an example is given to show that there exist someâ… -flat moduleswhich are not flat module.Then definitions ofâ… -flat dimension,â… -week dimension and faithfullâ… -flat modules are given and their properties are discussed.