A Study of Noetherian and Artinian (R,S)-Modules

Authors

  • Dian Ariesta Yuwaningsih Department of Mathematics Education, Universitas Ahmad Dahlan, Yogyakarta
  • Yassin Dwi Cahyo Department of Mathematics, Universitas Diponegoro, Semarang
  • Gusti Ayu Dwi Yanti Department of Mathematics, Universitas Gadjah Mada, Yogyakarta
  • Rima Aksen Cahdriyana Department of Mathematics Education, Universitas Ahmad Dahlan, Yogyakarta
  • Dea Apriani Department of Mathematics Education, Universitas Ahmad Dahlan, Yogyakarta

DOI:

https://doi.org/10.20956/j.v22i1.45166

Keywords:

Noetherian, Artinian, (RS)-modul

Abstract

As science develops, a module has been generalized to a new algebraic structure called -module. Some of the concepts in the module can also be extended into the -module structure. The concepts related to the Noetherian module and the Artinian module have never been developed into the -module structure. Therefore, this study aims to examine the development results related to the Noetherian module and the Artinian module in the -module. In this paper, we present the definition of Noetherian -module, the definition of Artinian -module, and the development results of its properties in the -module structure.

References

[1] Yuwaningsih, D.A. & Wijayanti, I.E., 2015. On Jointly Prime Radicals of (R,S)-Modules, Journal of the Indonesian Mathematical Society, Vol.21, No.1, 25-34.

[2] Yuwaningsih, D.A., Wijayanti, I.E., & Prasetyo, P.W., 2019. On (R,S)-Modules Homomorphisms. IOP Conf. Series: Journal of Physics: Conf.Series, Vol.1188, 012114.

[3] Yuwaningsih, D.A., 2020. Hasil Tambah Langsung Suatu (R,S)-Modul. Journal of Fundamental Mathematics and Applications, Vol.3, No.2, 98-106.

[4] Wijayanti, I.E., Wahyuni, S., Yuwaningsih, D.A. & Hartanto, A.D., 2016. Teori Ring dan Modul. Gama Press UGM, Yogyakarta.

[5] Khumprapussorn, T., Pianskool, S., & Hall, M., 2012. (R,S)-Modules and their Fully and Jointly Prime Submodules. International Mathematical Forum, Vol.7, No.33, 1631-1643.

[6] Adkins, W.A., 1992. Algebra “An Approach via Module Theory”. Springer-Verlag New York, Inc., USA.

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Published

2025-09-08

How to Cite

Yuwaningsih, D. A., Cahyo, Y. D., Yanti, G. A. D., Cahdriyana, R. A., & Apriani, D. (2025). A Study of Noetherian and Artinian (R,S)-Modules . Jurnal Matematika, Statistika Dan Komputasi, 22(1), 149–158. https://doi.org/10.20956/j.v22i1.45166

Issue

Vol. 22 No. 1 (2025): SEPTEMBER 2025

Section

Research Articles

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

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