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/r is regular and r = JacS, where S is the ring of all R -endomorphisms of M and r = {φ 2 S | Im φ ⌧ M }. 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.

A NOTE ON NONCOSINGULAR LIFTING MODULES ПРО НЕКОСИНГУЛЯРНI МОДУЛI IЗ ВЛАСТИВIСТЮ ПIДНЯТТЯ Let R be a right perfect ring. Let M be a noncosingular lifting module which does not have any relatively projective component. Then M has finite hollow dimension. Нехай R-праве досконале кiльце, а M-некосингулярний модуль iз властивiстю пiдняття, що не має жодної вiдносно проективної компоненти. Тодi M має скiнченну дуальну розмiрнiсть Голдi.