Ukrainian Mathematical Journal

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

A Generalization of Lifting Modules

  • T. Amouzegar Kalati

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.


Direct Summand Projective Module Division Ring Regular Ring Cyclic Module 
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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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