Some Properties of Prime Submodules and the Effect of Localization on Their Structures

Hazhar Ali  Said; Adil Kadir  Jabbar

doi:10.24996/ijs.2026.67.6.32

Authors

Hazhar Ali Said Department of Mathematics, College of Basic Education, University of Raparin
Adil Kadir Jabbar Department of Mathematics, College of Science, University of Sulaimani

DOI:

https://doi.org/10.24996/ijs.2026.67.6.32

Keywords:

Maximal submodules, prime submodules, gw-prime submodules, multiplicative systems, localization

Abstract

In this paper, prime modules are studied and investigated. Some properties of this type of submodules are proved. Some conditions are given under which every submodule of a prime submodule is maximal and some conditions are given which make every proper submodule of prime modules as a prime submodule. It is proved that multiplication modules in which prime submodules are finitely generated are Noetherian. In addition, the effects of localization on prime submodules are studied and some results concerning the localization of prime submodules are proved.

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Published

2026-06-30

Issue

Vol 67 No 6 (2026)

Section

Mathematics

License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

[1]

H. A. . Said and A. K. . Jabbar, “Some Properties of Prime Submodules and the Effect of Localization on Their Structures”, Iraqi Journal of Science, vol. 67, no. 6, pp. 3458–3470, Jun. 2026, doi: 10.24996/ijs.2026.67.6.32.