Rejection lemma and almost split sequences - Drozd, Yu. A. (Ukrains’kyi Matematychnyi Zhurnal, 2021)
UDC 512.55We study the behavior of almost split sequences and Auslander – Reiten quivers of an order under rejection of bijective modules as defined in [Ю. А. Дрозд, В. В. Кириченко, О квазибассовых порядках, Изв. АН СССР. Сер. мат., 36, 328 – 370 (1972)]. In particular, we establish relations of stable categories and almost split sequences for an order $A$ and the order $A′$ obtained from $A$ by such a rejection. These results are refined for the Gorenstein and Frobenius cases.