TY - JOUR ID - TI - On µ-lifting Modules AU - Wasan Khalid AU - Enas Mustafa Kamil PY - 2019 VL - 60 IS - 2 SP - 371 EP - 380 JO - Iraqi Journal of Science المجلة العراقية للعلوم SN - 00672904 23121637 AB - Let R be a ring with identity and let M be a left R-module. M is called µ-lifting modulei f for every sub module A of M, There exists a direct summand D of M such that M = D D', for some sub module D' of M such that A≤D and A D'<<µ D'. The aim of this paper is to introduce properties of µ-lifting modules. Especially, we give characterizations of µ-lifting modules. On the other hand, the notion of amply µ-supplemented iis studied as a generalization of amply supplemented modules, we show that if M is amply µ-supplemented such that every µ-supplement sub module of M is a direct summand, then M is µ-lifting module. Finally, we give some conditions under which the quotient and direct sum of µ-lifting modules is µ-lifting.

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