完全AC分解

Complete AC Resolution

首先,引入复形的Gorenstein AC平坦维数的定义,并对任意复形M,给出GF ac-dim M≤n的刻画;其次,证明若复形M有有限的Gorenstein AC平坦维数,则M存在一个完全AC分解T→τF→πM.

Firstly,we introduced the definition of Gorenstein AC flat dimension for complexes and gave some characterizations of GF ac-dim M≤n for any complex M.Secondly,we proved that if the complex M had finite Gorenstein AC flat dimension,then M had a complete AC resolution T→τF→πM.