nZ-Gorenstein cluster tilting subcategories

Abstract

Let Λ be an Artin algebra. In this paper, the notion of nZ-Gorenstein cluster tilting subcategories will be introduced. It is shown that every nZ-cluster tilting subcategory of mod-Λ is nZ-Gorenstein if and only if Λ is an Iwanaga-Gorenstein algebra. Moreover, it will be shown that an nZ-Gorenstein cluster tilting subcategory of mod-Λ is an nZ-cluster tilting subcategory of the exact category Gprj-Λ, the subcategory of all Gorenstein projective objects of mod-Λ. Some basic properties of nZ-Gorenstein cluster tilting subcategories will be studied. In particular, we show that they are n-resolving, a higher version of resolving subcategories. © 2021 Elsevier Inc.