模和环的(m,n)-余挠维数

The (m,n)-cotorsion dimensions of modules and rings

设m,n是两个任意取定的正整数,引入了模与环的(m,n)-余挠维数,证明了在稍强(m,n)-凝聚环上,模与环的(m,n)-余挠维数许多类似于经典同调维数的性质,给出了稍强(m,n)-凝聚环是von-Neumann正则环的一些等价刻画。

Let m, n be two given positive integers. It is shown that over slightly(m,n)-coherent rings, the(m,n)-cotorsion dimensions of modules and rings share many nice properties as the classical homological dimensions. Some equivalent characterizations that slightly(m,n)-coherent rings are von-Neumann regular rings are given.