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A Generalization of Lifting Modules

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We introduce the notion of I -lifting modules as a proper generalization of the notion of lifting modules and present some properties of this class of modules. It is shown that if M is an I -lifting direct projective module, then S/▽ is regular and ▽ = JacS, where S is the ring of all R-endomorphisms of M and ▽ = {ϕS | Im ϕM}. Moreover, we prove that if M is a projective I -lifting module, then M is a direct sum of cyclic modules. The connections between I -lifting modules and dual Rickart modules are presented.

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Correspondence to T. Amouzegar Kalati.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 11, pp. 1477–1484, November, 2014.

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Amouzegar Kalati, T. A Generalization of Lifting Modules. Ukr Math J 66, 1654–1664 (2015). https://doi.org/10.1007/s11253-015-1042-z

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Keywords

  • Direct Summand
  • Projective Module
  • Division Ring
  • Regular Ring
  • Cyclic Module