On Jointly ?-Prime (R,S)-Submodules

Authors

  • Dian Ariesta Yuwaningsih Universitas Ahmad Dahlan
  • Fayi Salsabila Sumaryati Universitas Ahmad Dahlan

DOI:

https://doi.org/10.20956/j.v19i2.24291

Keywords:

prime, ?-prime, (?, ?)-module, ?-prime (?, ?)-submodule

Abstract

Given ? and ? be commutative ring with unity. The (?, ?)-bimodule structure has beengeneralized into the (?, ?)-module structure. Likewise, primeness in a module has also beengeneralized to the (?, ?)-module structure. However, the existing prime definition onlyfocuses on scalar multiplication operations in modules. The ?-prime submodule is one of thegeneralizations of the prime submodule, which involves additive operations and scalarmultiplication in the module. This article presents a generalization of the ?-prime submodulesinto the (?, ?)-module structure, hereinafter referred to as the jointly ?-prime (?, ?)-submodules. Furthermore, at the end of this article some properties of the jointly ?-prime(?, ?)-submodule are presented.

Downloads

Download data is not yet available.

References

Behboodi, M. and Koohy, H., 2004, Weakly Prime Modules, Vietnam Journal of Mathematics, Vol. 32, No. 2, Hal. 185-195.

Dauns, J., 1978, Prime Modules, Journal fur die reine and angewandte Mathematik, No. 298, Hal. 156-181.

Ferrero, M. dan Rodrigues, V., 2006, On Prime and Semiprime Modules and Comodules, Journal of Algebra and Its Applications, Vol. 5, No. 5, Hal. 681-694.

Haghany, A. dan Vedadi, R., 2005, Endoprime Modules, Acta Math. Hungar., Vol 106, No. 1-2, Hal. 89-99.

Khumprapussorn, T., 2018, On α-Prime and Weakly α-Prime Submodules, European Journal of Pure and Applied Mathematics, Vol. 11, No. 3, Hal. 730-739.

Khumprapussorn, T., 2019, On β-Prime Submodules, Journal of the Indonesian Mathematical Society, Vol. 25, No. 02, Hal. 128-138.

Khumprapussorn, T., Pianskool, S., dan Hall, M., 2012, (R,S)-Modules and Their Fully and Jointly Prime Submodules, International Mathematical Forum, Vol. 7, No. 33, Hal. 1631-1643.

Khumprapussorn, T., 2013, Left R-Prime (R,S)-Modules, International Mathematical Forum, Vol. 8, No. 13, Hal. 619-626.

Wijayanti, I.E., 2006, Coprime Modules and Comodules, Dissertation, University of Dusseldorf, Germany.

Yassemi, S., 2001, The Dual Notion of Prime Submodules, Archivum Mathematicum, Vol. 37, No. 4, Hal. 273-278.

Yuwaningsih, D.A., Rusmining, dan Puguh, W.P., 2021, Beberapa Sifat (R,S)-Submodul Prima-α Gabungan, Journal of Fundamental Mathematics and Applications (JFMA), Vol. 4, No. 2, Hal. 167-179.

Yuwaningsih, D.A., Wijayanti, I.E., dan Prasetyo, P.W., 2019, On (R,S)-Module Homomorphisms, J. Phys. Conf. Ser., vol. 1188, no. 1.

Downloads

Published

2023-01-05

How to Cite

Yuwaningsih, D. A., & Sumaryati, F. S. (2023). On Jointly ?-Prime (R,S)-Submodules. Jurnal Matematika, Statistika Dan Komputasi, 19(2), 423-432. https://doi.org/10.20956/j.v19i2.24291

Issue

Vol. 19 No. 2 (2023): JANUARY 2023

Section

Research Articles

License

Copyright (c) 2023 Author and publisher

Creative Commons License

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

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

Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license.  This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.