H-Pu-supplemented modules
*Halah Qahtan HamdiCorresponding authorhala.hamdi@sc.uobaghdad.edu.iqDepartment of MathematicsCollege of ScienceUniversity of BaghdadBaghdad, IraqView full profile → , Nuhad S. Al-Mothafarnuhad.salim@sc.uobaghdad.edu.iqDepartment of MathematicsCollege of ScienceUniversity of BaghdadBaghdad, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Mar 2025
- Published Online:
- 15 Jan 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2322
- Pages:
- 179–184
Abstract
Keywords
Subject Classifications
References
[1] Friedrich Kasch, Modules and Rings, vol. 17. New York, NY, USA: Academic Press (1982).
[2] Ahmed Kabban and Waleed Khalid, “On Jacobson-small submodules,” Iraqi Journal of Science, vol. 60, no. 7, pp. 1584–1591 (2019), doi: 10.24996/ijs. 2019.60.7.18.
[3] Mohammed Abbas Ahmed, Ismail Abbas Dhari, and Zainab Abdul Atiya, “Purely small submodules and purely hollow modules,” Iraqi Journal of Science, vol. 63, no. 12, pp. 5487–5495 (2022), doi: 10.24996/ijs . 2022.63.12.34.
[4] Salah Hassan Mohamed and Bruno J. Müller, Continuous and Discrete Modules, London Mathematical Society Lecture Note Series, vol. 147. Cambridge, U.K.: Cambridge University Press (1990).
[5] Dongsheng Wu, “Cofinitely H-supplemented modules,” Southeast Asian Bulletin of Mathematics, vol. 35, no. 3, pp. 529–535 (2011).
[6] Hussein Qasim Hamdi and Noor Sabah Al-Mothafar, “Pu-supplement sub-modules,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 4-B, pp. 1343–1353 (2025).
[7] Yong Wang and Dongsheng Wu, “On H-supplemented modules,” Communications in Algebra, vol. 40, no. 10, pp. 3679–3689 (2012).
[8] John Clark, Claudia Lomp, Natarajan Vanaja, and Robert Wisbauer, Lifting Modules: Supplements and Projectivity in Module Theory, Frontiers in Mathematics. Basel, Switzerland: Birkhäuser, pp. 1–407 (2006), doi: 10.1007/3-7643-7573-6.
[9] Kamal Ahmmed and Noor Sabah Al-Mothafar, “Pr-small R-submodules of modules and Pr-radicals,” Journal of Interdisciplinary Mathematics, vol. 26, no. 7, pp. 1511–1516 (2023).
[10] Adnan Ghazi Nauom and Bahar Hassan Al-Bahranny, “Modules with pure sum property,” Iraqi Journal of Science, vol. 43, no. 3, pp. 1–10 (2002).
[11] Veli Erdoğdu, “Distributive modules,” Canadian Mathematical Bulletin, vol. 30, no. 2, pp. 248–254 (1987).
[12] Ali Cem Özcan, Abdullah Harmanci, and Patrick F. Smith, “Duo modules,” Glasgow Mathematical Journal, vol. 48, no. 3, pp. 533–545 (2006).
[13] I. H. Muslem, “Some types of retractable and compressible modules,” M.S. thesis, College of Education for Pure Science, University of Baghdad, Baghdad, Iraq (2016).
[14] Neslihan Orhan, Dilek K. Tütüncü, and Rachid Tribak, “On hollow-lifting modules,” Taiwanese Journal of Mathematics, vol. 11, no. 2, pp. 545–568 (2007).
[15] S. A. Al-Ameedee and A. J. Obaid, “Sandwich results of meromorphic multivalent functions defined by multiplier transform,” Journal of Interdisciplinary Mathematics, vol. 26, no. 4, pp. 651–658 (2023), doi: 10.47974/JIM-1484.
[16] A. A. A. Zyarah and N. S. Al-Mothafar, “On primary radical RΓ-submodules of RΓ-modules,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 23, no. 5, pp. 1001–1007 (2020).




