Homology theories and Gorenstein dimensions for complexes

TL;DR

This paper explores advanced homology theories and Gorenstein dimensions for complexes, establishing new relations and improvements in understanding their properties in module theory.

Contribution

It introduces new insights into Gorenstein projective/flat dimensions for complexes and enhances existing results on Tate, stable, and unbounded homology.

Findings

Relations between Gorenstein dimensions for complexes and modules clarified

Improved results on Tate, stable, and unbounded homology for modules

Enhanced understanding of homology theories in the context of complexes

Abstract

In this paper, we first study the Gorenstein projective/flat dimension of complexes of modules. The relation between the Gorenstein projective/flat dimension for complexes and that for modules are investigated. Then we study Tate, stable and unbounded homology for complexes of modules. In the case of module arguments, we get some results that improve the known results.