Rafail AlizadeYilmaz M. DemirciYilmaz DurgunDilek PusatPusat, DilekDurǧun, YilmazAlizade, RafailDemirci, Yilmaz M.2025-10-0620140092-78721532-412510.1080/00927872.2012.6995672-s2.0-84886412650http://dx.doi.org/10.1080/00927872.2012.699567https://gcris.yasar.edu.tr/handle/123456789/6701https://doi.org/10.1080/00927872.2012.699567We show that for hereditary rings the smallest proper classes containing respectively the classes of short exact sequences determined by small submodules submodules that have supplements and weak supplement submodules coincide. Moreover we show that this class can be obtained as a natural extension of the class determined by small submodules. We also study injective projective coinjective and coprojective objects of this class. We prove that it is coinjectively generated and its global dimension is at most 1. Finally we describe this class for Dedekind domains in terms of supplement submodules.Englishinfo:eu-repo/semantics/openAccessCoatomic modules, Coatomic supplement submodule, Coinjective modules, Coprojective modules, Extended weak supplement, Proper class of short exact sequences, Weak supplement submodule, Primary 18G25, Secondary 13C60, 16D90MODULESCoatomic Supplement SubmoduleProper Class of Short Exact SequencesWeak Supplement SubmoduleCoprojective ModulesPrimary 18G2516D90Coinjective ModulesSecondary 13C60Extended Weak SupplementCoatomic ModulesArticle