Cofinitely \(F\)-supplemented modules
type: Item
instance of: scholarly article
title: Cofinitely \(F\)-supplemented modules
author: Salahattin Özdemir
published in: São Paulo Journal of Mathematical Sciences
publication date: 2024-07-03T00:00:00Z
review text: Let \(R\) be a unital ring, \(M\) a left \(R\)-module, and \(U,\, V\) and \(F\) submodules of \(M\) with \(F\) proper. \(V\) is an \(F\)-supplement of \(U\) in \(M\) if \(V\) is minimal in the collection of submodules \(F\subseteq X \subset M\) such that \(M = U + X\). The submodule \(U\) has ample \(F\)-supplements in \(M\) if every submodule \(V\) such that \(M = U + V\) contains an \(F\)-supplement of \(U\) in \(M\). The module \(M\) is called (amply) \(F\)-supplemented if every submodule of \(M\) has an (ample) F-supplement in \(M\). \(U\) is cofinitely generated if \(M/U\) is finitely generated. If every cofinite submodule of \(M\) has an (ample) \(F\)-supplement, then \( M\) is an (amply) cofinitely \(F\)-supplemented module.\N\NThe author proves several properties of (amply) (cofinitely) \(F\)-supplemented modules, and characterises them in terms of their submodules and factor modules.
reviewed by: Phillip Schultz
Mathematics Subject Classification ID: 16D10
Mathematics Subject Classification ID: 16D80
zbMATH DE Number: 7875530
zbMATH Keywords: \(F\)-supplement submodule
zbMATH Keywords: cofinitely \(F\)-supplemented module
MaRDI profile type: Publication
cites work: MODULES WHOSE MAXIMAL SUBMODULES HAVE SUPPLEMENTS
cites work: Co-coatomically supplemented modules
cites work: On generalizations of essential and small submodules
cites work: Q5471610
cites work: Q5214061
cites work: Eine Kennzeichnung Semi-perfekter Moduln
cites work: F-supplemented modules
cites work: Rad-discrete modules
cites work: Q4002547
DOI: 10.1007/S40863-023-00388-2
description: scientific article; zbMATH DE number 7875530