H-supplemented modules with respect to images of fully invariant submodules

Abstract Lifting modules plays important roles in module theory. H-supplemented modules are a nice generalization of lifting modules which have been studied extensively recently. In this article, we introduce a proper generalization of H-supplemented modules via images of fully invariant submodules....

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Autores principales:	Moniri Hamzekolaee,A. R., Amouzegar,T.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2021
Materias:	H-supplemented module IF -lifting module IF-H-supplemented module Dual Rickart module Endomorphisms ring.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000100035
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spelling	oai:scielo:S0716-091720210001000352021-01-26H-supplemented modules with respect to images of fully invariant submodulesMoniri Hamzekolaee,A. R.Amouzegar,T. H-supplemented module IF -lifting module IF-H-supplemented module Dual Rickart module Endomorphisms ring. Abstract Lifting modules plays important roles in module theory. H-supplemented modules are a nice generalization of lifting modules which have been studied extensively recently. In this article, we introduce a proper generalization of H-supplemented modules via images of fully invariant submodules. Let F be a fully invariant submodule of a right Rmodule M. We say that M is I F -H-supplemented in case for every endomorphism φ of M, there is a direct summand D of M such that φ(F) + X = M if and only if D + X = M, for every submodule X of M. It is proved that M is I F -H-supplemented if and only if F is a dual Rickart direct summand of M for a fully invariant noncosingular submodule F of M. It is shown that the direct sum of I F -H supplemented modules is not in general I F -H-supplemented. Some sufficient conditions such that the direct sum of I F -H-supplemented modules is I F -H-supplemented are given.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.1 20212021-02-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000100035en10.22199/issn.0717-6279-2021-01-0003
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	H-supplemented module IF -lifting module IF-H-supplemented module Dual Rickart module Endomorphisms ring.
spellingShingle	H-supplemented module IF -lifting module IF-H-supplemented module Dual Rickart module Endomorphisms ring. Moniri Hamzekolaee,A. R. Amouzegar,T. H-supplemented modules with respect to images of fully invariant submodules
description	Abstract Lifting modules plays important roles in module theory. H-supplemented modules are a nice generalization of lifting modules which have been studied extensively recently. In this article, we introduce a proper generalization of H-supplemented modules via images of fully invariant submodules. Let F be a fully invariant submodule of a right Rmodule M. We say that M is I F -H-supplemented in case for every endomorphism φ of M, there is a direct summand D of M such that φ(F) + X = M if and only if D + X = M, for every submodule X of M. It is proved that M is I F -H-supplemented if and only if F is a dual Rickart direct summand of M for a fully invariant noncosingular submodule F of M. It is shown that the direct sum of I F -H supplemented modules is not in general I F -H-supplemented. Some sufficient conditions such that the direct sum of I F -H-supplemented modules is I F -H-supplemented are given.
author	Moniri Hamzekolaee,A. R. Amouzegar,T.
author_facet	Moniri Hamzekolaee,A. R. Amouzegar,T.
author_sort	Moniri Hamzekolaee,A. R.
title	H-supplemented modules with respect to images of fully invariant submodules
title_short	H-supplemented modules with respect to images of fully invariant submodules
title_full	H-supplemented modules with respect to images of fully invariant submodules
title_fullStr	H-supplemented modules with respect to images of fully invariant submodules
title_full_unstemmed	H-supplemented modules with respect to images of fully invariant submodules
title_sort	h-supplemented modules with respect to images of fully invariant submodules
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2021
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000100035
work_keys_str_mv	AT monirihamzekolaeear hsupplementedmoduleswithrespecttoimagesoffullyinvariantsubmodules AT amouzegart hsupplementedmoduleswithrespecttoimagesoffullyinvariantsubmodules
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H-supplemented modules with respect to images of fully invariant submodules

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