TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

On e*-singular lifting modules

* ,

* Corresponding author · click or hover a name for details

pp. 161–167Vol. 29Issue 1January 2026DOI: 10.47974/JDMSC-2319 Crossmark XML
Received:
12 Mar 2025
Published Online:
15 Jan 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2319
Pages:
161–167

Abstract

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.

Keywords

Subject Classifications

Primary 93A30Secondary 49K15

References

[1] K. Ahmmed and N. S. Al.Mothafar, “Pr-small R-submodules of modules and Pr-radicals.,” Journal of Interdisciplinary Mathematics, vol. 26, no. 7, pp. 1511–1516 (2023).
[2] F. Kasch, Modules and Rings, Acad. Press, London (1982).
[3] H. R. Baanoon, “e∗-Essential submodule,” European Journal of Pure Applied. Math., vol. 15, no. 1, pp. 224–228 (2022). 
[4] K. Goodearl, Ring Theory: Nonsingular Rings and Modules, Marcel Dekker, New York (1976).
[5] A. Kabban and W. Khalid, “On e*_Singular Small Submodules,” AIP Conf. Proceeding, vol. 3264, no. 1, pp. 050063 (1-6) (2025).
[6] A. Kabban and W. Khalid, “e*Singular–Hollow Modules and e*Singular–Coclosed Submodules,” Iraqi Journal of Science, Vol. 66, No. 6, pp. 2477-2486, (2025).
[7] J. Clark, C. Lomp, and R. Wisbauer, Lifting Modules: Supplements and Projectivity in Module Theory, Frontiers in Math., Birkhauser (2006).
[8] E. M. Kamil and W. Hasan, “On µ-lifting modules,” Iraqi Journal of Science, vol. 60, no. 2, pp. 371–380 (2019).
[9] A. Kabban and W. Khalid, “On e*Singular–Supplement Submodules,” Iraqi Journal of Science, Vol. 66, No. 12, pp. 5660-5674, (2025).
[10] A. A. Abduljaleel and S. M. Yaseen, “On Large-Lifting and Large-Supplemented Modules,” Iraqi Journal of Science, vol. 63, no. 4, pp. 1729–1735 (2022).
[11] A. A. Elewi and T. A. Ibrahiem, “On δ*-Supplemented Modules,” Baghdad Science Journal, vol. 17, no. 1, pp. 136–140 (2020).
[12] N. Orhan, D. K. Tütüncü, and R. Tribak, “On hollow-lifting modules,” Taiwan. J. Math., vol. 11, no. 2, pp. 545–568 (2007).

Views: 94Downloads: 6Citations: 0