We study the behavior of almost split sequences and Auslander–Reiten quivers of the orders under rejection of bijective modules as defined in [Yu. A. Drozd and V. V. Kirichenko, Izv. Akad. Nauk SSSR, Ser. Mat., 36, 328 (1972)]. In particular, we establish the relations for stable categories and almost split sequences of an order A and the order A′ obtained from A by the indicated rejection. These results are improved for the Gorenstein and Frobenius cases.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 6, pp. 780–798, June, 2021. Ukrainian DOI: 10.37863/umzh.v73i6.6580.
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Drozd, Y.A. Rejection Lemma and Almost Split Sequences. Ukr Math J 73, 908–929 (2021). https://doi.org/10.1007/s11253-021-01967-2
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DOI: https://doi.org/10.1007/s11253-021-01967-2