Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5638
Title: The proper class generated by weak supplements
Authors: Alizade, Rafail
Demirci, Yılmaz Mehmet
Durğun, Yılmaz
Pusat, Dilek
Keywords: Coatomic modules
Coatomic supplement submodule
Coinjective modules
Weak supplement submodule
Extended weak supplement
Issue Date: Jan-2014
Publisher: Taylor and Francis Ltd.
Source: Alizade, R., Demirci, Y.M., Durǧun, Y., and Pusat, D. (2014). The proper class generated by weak supplements. Communications in Algebra, 42(1), 56-72. doi:10.1080/00927872.2012.699567
Abstract: 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.
URI: https://doi.org/10.1080/00927872.2012.699567
http://hdl.handle.net/11147/5638
ISSN: 0092-7872
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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