Article
Kyungpook Mathematical Journal 2020; 60(4): 673-682
Published online December 31, 2020
Copyright © Kyungpook Mathematical Journal.
Direct Sums of Strongly Lifting Modules
Shahabaddin Ebrahimi Atani, Mehdi Khoramdel* and Saboura Dolati Pishhesari
Department of Mathematics, University of Guilan, P. O. Box 1914, Rasht, Iran
e-mail : ebrahimi@guilan.ac.ir, mehdikhoramdel@gmail.com and saboura_dolati@yahoo.com
Received: June 20, 2019; Revised: August 5, 2020; Accepted: August 18, 2020
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