The Proper Class Generated by Weak Supplements - Alizade, Rafail; Demirci, Yılmaz Mehmet; Pusat, Dilek; Durğun, Yılmaz; Pusat, Dilek; Alizade, Rafail (Taylor and Francis Ltd., 2014)
We 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.
Keywords: Coatomic modules; Coatomic supplement submodule; Coinjective modules; Weak supplement submodule; Extended weak supplement