journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2319 On e*-singular lifting modules Kabban Ali A. Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq Khalid Wasan Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq 29 1 161 167 15 01 2026

Any R-module G is named e*S-lifting module if each sub-module L of G, there is sub-module V of L such that G = V ⨁ D, where D ⊆ G and L ∩ D ≪e*S D. This work proposes to present characteristics and examples of e*S-lifting modules. We list few conditions that must be met for the quotient and direct sums of e*S-lifting modules to be e*S-lifting.

 e*S-Small sub-modules Lifting modules e*S-lifting modules e*S-hollow sub-modules access open retracted no