THE PROPER CLASS GENERATED BY WEAK SUPPLEMENTS

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Alizade R., Demirci Y. M., Durgun Y., Pusat D.

COMMUNICATIONS IN ALGEBRA, vol.42, no.1, pp.56-72, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.1080/00927872.2012.699567
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.56-72
  • Keywords: Coatomic modules, Coatomic supplement submodule, Coinjective modules, Coprojective modules, Extended weak supplement, Proper class of short exact sequences, Weak supplement submodule, Primary 18G25, Secondary 13C60, 16D90, MODULES
  • Çukurova University Affiliated: No

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.