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





H-supplemented module, IF -lifting module, IF-H-supplemented module, Dual Rickart module, Endomorphisms ring


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

Author Biographies

A. R. Moniri Hamzekolaee, University of Mazandaran.

Faculty of Mathematical Sciences, Dept. of Mathematics.

Tayyebeh Amouzegar, Quchan University of Technology.

Dept. of Mathematics.


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How to Cite

A. R. Moniri Hamzekolaee and T. Amouzegar, “H-supplemented modules with respect to images of fully invariant submodules”, Proyecciones (Antofagasta, On line), vol. 40, no. 1, pp. 35-48, Jan. 2021.