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Ukrainian Mathematical Journal

, Volume 66, Issue 11, pp 1654–1664 | Cite as

A Generalization of Lifting Modules

  • T. Amouzegar Kalati
Article
  • 98 Downloads

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.

Keywords

Direct Summand Projective Module Division Ring Regular Ring Cyclic Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • T. Amouzegar Kalati
    • 1
  1. 1.Quchan University of Advanced TechnologyQuchanIran

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