The Proper Class Generated by Weak Supplements

Autor:	Yilmaz Mehmet Demirci, Dilek Pusat, Yılmaz Durğun, Rafail Alizade
Přispěvatelé:	Demirci, Yılmaz Mehmet, Durğun, Yılmaz, Pusat, Dilek, Izmir Institute of Technology. Mathematics
Rok vydání:	2013
Předmět:	Coatomic supplement submodule Class (set theory) Pure mathematics Algebra and Number Theory Coinjective modules Weak supplement submodule Dedekind cut Extension (predicate logic) Extended weak supplement Coatomic modules Injective function Mathematics Global dimension
Zdroj:	Communications in Algebra. 42:56-72
ISSN:	1532-4125 0092-7872
DOI:	10.1080/00927872.2012.699567
Popis:	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. TUBITAK (107T709)
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1ab3fdad765f095d6ce9bfa78e2c72fc https://doi.org/10.1080/00927872.2012.699567 Zobrazit plný text záznamu