Syzygy properties under recollements of module categories

Abstract

Let [Formula: see text] be an artin algebra and [Formula: see text] be an idempotent ideal of [Formula: see text]. Then there is a recollement of [Formula: see text] relative to [Formula: see text] and [Formula: see text]. In this paper, we study some properties of Lat-syzygy-finite classes, special Lat-syzygy-finite classes and Lat-Igusa–Todorov classes. Then, we compare the algebras [Formula: see text], [Formula: see text] and [Formula: see text] with respect to Lat-syzygy-finite properties, special Lat-syzygy-finite properties and Lat-Igusa–Todorov properties under suitable conditions.