X-强n-Gorenstein投射模

X-strongly n-Gorenstein projective modules

设X是包含投射模的模类。引入X-强n-Gorenstein投射模的概念,给出了一些基本性质。证明了对非负整数n,R-模M的X-Gorenstein投射维数不超过n当且仅当M是某个X-强n-Gorenstein投射模的直和项。

Let X be a class of containing projective modules.In this paper,the concept of the X-strongly n-Gorenstein projective modules is introduced.We give some basic properties and prove that the X-Gorenstein projective dimension of a module M does not exceed a non-negative integer n if and only if M is the direct summand of a X-strongly n-Gorenstein projective module.