Analisis Submodul dan Sifat Keprimaan dalam Ruang Modul

Authors

  • Sefti Fajriatul Musyarrofah Universitas Mataram
  • I Gusti Yogananda Karang Universitas Mataram
  • Khairatun Hisan Universitas Mataram
  • Luzianawati Luzianawati Universitas Mataram

DOI:

https://doi.org/10.29303/smj.v2i1.262

Keywords:

Prime Submodule, Nearly Prime Submodule, Free Module, Torsion-Free Module, Annihilator

Abstract

This study analyzes prime submodules and primality properties in module spaces, fundamental topics in abstract algebra. The primary objective is to determine conditions for prime submodule formation in commutative rings and to examine their relationship with nearly prime submodules. The approach employed involves the decomposition of modules in principal ideal domains, with particular attention given to the concepts of annihilators, submodule orders, and the characteristics of torsion-free quotient modules. The findings indicate that nearly prime submodules can only be regarded as prime submodules in free modules. Furthermore, the module decomposition approach proves effective for gaining a comprehensive understanding of module structures. The concepts of annihilators and submodule orders provide profound insights into the relationships between module elements and ring elements. This study offers significant theoretical contributions to abstract algebra and establishes a foundation for further developments, particularly in applications related to number theory and cryptography.

References

J. Ambar and M. Afdhaluzzikri, “Studi Keprimaan dalam Modul : Submodul Prima , Prima Lemah , Hampir Prima , dan ? - Hampir Prima . ( Study of Primality in Modules : Prime , Weakly Prime , Almost Prime , and ? -Almost Prime Submodules ),” no. 2, 2024.

I. G. A. W. Wardhana, P. Astuti, and I. Muchtadi-Alamsyah, “The Characterization of Almost Prime Submodule on the Finitely Generated Module over Principal Ideal Domain,” Journal of the Indonesian Mathematical Society, vol. 30, no. 1, pp. 63–76, 2024, doi: 10.22342/jims.30.1.1396.63-76.

R. Juliana, I. G. A. W. Wardhana, and Irwansyah, “Some Characteristics of Cyclic Prime, Weakly Prime and Almost Prime Submodule of Gaussian Integer Modulo over Integer,” AIP Conf Proc, vol. 2329, no. February, 2021, doi: 10.1063/5.0042586.

I. G. A. W. Wardhana, N. W. Switrayni, and Q. Aini, “Eigen Mathematics Journal Submodul Prima Lemah dan Submodul Hampir Prima Pada Z-modul M2(Zn),” Eigen Mathematics Journal, vol. 1, no. 1, pp. 28–30, 2018.

M. Afdhaluzzikri and J. Ambar, “Karakteristik Beberapa Submodul dari Suatu Modul ( Some Characteristics of Submodules of Module ),” no. 2, 2024.

I. G. A. W. Wardhana, “The Decomposition of a Finitely Generated Module over Some Special Ring,” JTAM (Jurnal Teori dan Aplikasi Matematika), vol. 6, no. 2, pp. 261–267, 2022, doi: 10.31764/jtam.v6i2.6769.

D. I. Modul and D. A. N. Modul, “SUBMODUL PRIMA , SEMIPRIMA , DAN PRIMER,” vol. 2, pp. 1–10, 2017.

I. G. A. W. Wardhana, P. Astuti, and I. Muchtadi-Alamsyah, “The Characterization of Almost Prime Submodule on the Finitely Generated Module over Principal Ideal Domain,” Journal of the Indonesian Mathematical Society, vol. 30, no. 01, pp. 63–76, 2024.

H. A. Khashan, “On almost prime submodules,” Acta Mathematica Scientia, vol. 32, no. 2, pp. 645–651, Mar. 2012, doi: 10.1016/S0252-9602(12)60045-9.

S. Prima, P. Lemah, D. A. N. Hampir, D. Modul, M. Bilangan, and B. Modulo, “Submodul prima, prima lemah dan hampir prima dari modul matriks bilangan bulat modulo,” vol. 08, no. 02, pp. 136–141, 2024.

Downloads

Published

2025-04-30

How to Cite

Musyarrofah, S. F., Karang, I. G. Y., Hisan, K., & Luzianawati, L. (2025). Analisis Submodul dan Sifat Keprimaan dalam Ruang Modul. Semeton Mathematics Journal, 2(1), 53–59. https://doi.org/10.29303/smj.v2i1.262

Issue

Section

Articles