本项研究引入与相对同调理论相容的弱整闭性和星型算子方法，同时把交换环中的乘法理想理论方法，与Enochs、Holm等人建立的Gorenstein同调方法结合起来，形成新的研究方法，使之在刻画相对同调理论涉及的环结构发挥作用，解决环结构刻画中遇到的一些难题。研究内容有：（1）相对于相对同调理论的弱整闭性研究。（2）关于相对同调理论的局部整体原理的研究。（3）相对同调理论中的全局有限性的研究。（4）由超有限表现模确定同调理论研究。（4）低维（Gorenstein整体维数）环的结构刻画，特别是Ggldim(R)和Gwdim(R)不超过2的局部环的刻画。

This project introduces the method of weak integral closeness and star-operations compatible with relative homological theory, and combines the method of multiplicative ideal theory in commutative rings with Gorenstein homological method built by Enochs and Holm et al., and then forms a new study method. We hope that this new method can be used to characterize the structure of rings involved with relative homological theory and solve some difficult problems in characterizing the structure of rings. The major research content of this project includes the study of the weak integral closeness related to the relative homological theory, the local-global principle for the relative homological theory, the global finiteness in the relative homological theory, and the homological theory determined by the class of super finitely presented modules, and the characterization of the structure of the rings with small (Gorenstein global) dimension, especially the characterization of the commutative local rings of (weak) Gorenstein global dimension at most two.