Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Direct Sums of Strongly Lifting Modules

  • Received : 2019.06.20
  • Accepted : 2020.08.18
  • Published : 2020.12.31
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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.

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Acknowledgement

We would like to thank the referees for valuable comments.

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