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 |
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 |
Show full item record
CORE Recommender
SCOPUSTM
Citations
6
checked on Nov 2, 2024
WEB OF SCIENCETM
Citations
6
checked on Oct 26, 2024
Page view(s)
210
checked on Nov 4, 2024
Download(s)
264
checked on Nov 4, 2024
Google ScholarTM
Check
Altmetric
Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.