Gillespie所提出一个问题的否定回答

A negative answer to a question of Gillespie

本文引入Gorenstein n-凝聚环的概念,证明即使所有左R-模的AC-内射复形和所有内射左R-模的复形对应的同伦范畴是一致的,环R也未必是左凝聚的,从而否定地回答了Gillespie(2017)提出的一个问题.

In this paper, we introduce the notion of Gorenstein n-coherent rings and obtain that, even if the homotopy categories of all AC-injective complexes of left R-modules and all complexes of injective left R-modules coincide, R is not necessarily left coherent. This gives a negative answer to a question posed by Gillespie（2017）.