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Weak lifting modules with small radical

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Abstract

Keskin and Tribak (2005) studied the structure of weak lifting modules with small radicals over commutative noetherian (local) rings. They proved that a module M is weak lifting if and only if M is a direct sum of local modules of some special type. Such modules were further studied by Tribak (2007). In this note we study weak lifting modules M with small radical over arbitrary rings. We prove that M is an irredundant sum M =Σi∈I Mi where each Mi is local andΣi∈F Mi is a summand of M for every finite subset F of I. Moreover Σi∈F Mi = ⊕i∈F Ki with Ki local. In particular a finitely generated weak lifting module is a direct sum of local modules. This generalizes the analogous result for finitely generated lifting modules.

Original languageEnglish
Title of host publicationRing and Module Theory
EditorsToma Albu, Gary F. Birkenmeier, Ali Erdoǧan, Adnan Tercan
PublisherSpringer International Publishing
Pages129-134
Number of pages6
ISBN (Print)9783034600064
DOIs
Publication statusPublished - 2010
EventInternational Conference on Ring and Module Theory, 2008 - Ankara, Turkey
Duration: 18 Aug 200822 Aug 2008

Publication series

NameTrends in Mathematics
Volume50
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Conference

ConferenceInternational Conference on Ring and Module Theory, 2008
Country/TerritoryTurkey
CityAnkara
Period18/08/0822/08/08

Keywords

  • Weak lifting module

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