A new approach to H-supplemented modules via homomorphisms

Hamzekolaee, Ali Reza Moniri; Harmanci, Abdullah; Talebi, Yahya; Üngör, Burcu

doi:10.3906/mat-1709-74

Cited by 3 publications

(1 citation statement)

References 9 publications

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“…The author showed that a projective I-lifting module is a direct sum of cyclic modules. In [10], the authors studied H-supplemented modules via homomorphisms, which generalizes both H-supplemented modules and I-lifting modules. They called a module M , endomorphism H-supplemented (E-H-supplemented, for short) provided for every ϕ in End…”

Section: Introductionmentioning

confidence: 99%

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

Hamzekolaee

Amouzegar

2021

Proyecciones (Antofagasta)

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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 IF -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 IF -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 IF –H supplemented modules is not in general IF -H-supplemented. Some sufficient conditions such that the direct sum of IF -H-supplemented modules is IF -H-supplemented are given

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Section: Introductionmentioning

confidence: 99%