Three results on extension dimensions of syzygy module categories

Abstract

This paper establishes three main results on the extension dimension of syzygy module categories:(1)we prove that excellent ring extensions preserve extension dimensions of syzygy module categories,including syzygy categories of modules of finite projective dimensions;(2) for cleft extensions, we investigate the behavior of extension dimensions under natural nilpotency and projective conditions;(3)for commutative Artin rings, we establish local-global characterisations for the extension dimension.