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http://dx.doi.org/10.5666/KMJ.2020.60.4.673

Direct Sums of Strongly Lifting Modules  

Atani, Shahabaddin Ebrahimi (Department of Mathematics, University of Guilan)
Khoramdel, Mehdi (Department of Mathematics, University of Guilan)
Pishhesari, Saboura Dolati (Department of Mathematics, University of Guilan)
Publication Information
Kyungpook Mathematical Journal / v.60, no.4, 2020 , pp. 673-682 More about this Journal
Abstract
For the recently defined notion of strongly lifting modules, it has been shown that a direct sum is not, in general, strongly lifting. In this paper we investigate the question: When are the direct sums of strongly lifting modules, also strongly lifting? We introduce the notion of a relatively strongly projective module and use it to show if M = M1 ⊕ M2 is amply supplemented, then M is strongly lifting if and only if M1 and M2 are relatively strongly projective and strongly lifting. Also, we consider when an arbitrary direct sum of hollow (resp. local) modules is strongly lifting.
Keywords
lifting modules; strongly lifting modules; coclosed submodules; hollow modules; relatively strongly projective modules;
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