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 been
generalized into the (?, ?)-module structure. Likewise, primeness in a module has also been
generalized to the (?, ?)-module structure. However, the existing prime definition only
focuses on scalar multiplication operations in modules. The ?-prime submodule is one of the
generalizations of the prime submodule, which involves additive operations and scalar
multiplication in the module. This article presents a generalization of the ?-prime submodules
into 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.

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.

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Published

2023-01-05

Issue

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

Section

Research Articles

License

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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.

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