Generalizations of graded S-primary ideals
DOI:
https://doi.org/10.22199/issn.0717-6279-5357Keywords:
graded weakly S-prime ideals, weakly S-primary ideals, graded weakly primary ideals, graded S-primary ideals, graded weakly S-primary idealsAbstract
The goal of this article is to present the graded weakly S-primary ideals and graded g-weakly S-primary ideals which are extensions of graded weakly primary ideals. We state P is a graded weakly S-primary ideal of R if there exists s ∈ S such that for all x,y ∈ h(R), if 0 ̸= xy ∈ P, then sx ∈ P or sy ∈ Grad(P). Several properties and characteristics of graded weakly S-primary ideals as well as graded g-weakly S-primary ideals are investigated.
References
R. Abu-dawwas and M. Bataineh, “Graded r-ideals”, Iranian Journal of Mathematical Sciences and Informatics, vol. 14, no. 2, pp. 1-8, 2019. [On line]. Available: https://bit.ly/3fsADI3
A. S. Alshehry, “On graded S-primary ideals”, Mathematics, vol. 9, no. 20, p. 2637, 2021. https://doi.org/10.3390/math9202637
S. E. Atani, “On graded weakly primary ideals”, Quasigroups and related systems, vol. 13, no. 2, pp. 185-191, 2005. [On line]. Available: https://bit.ly/3DyJKiq
M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra. Reading: Addison-Wesley, 1969.
M. Bataineh and S. Kuhail, “Generalizations of primary ideals and submodules”, International Journal of Contemporary Mathematical Sciences, vol. 6, no. 17, pp. 811-824, 2011. [On line]. Available: https://bit.ly/3DCQziG
E. Y. Celikeli and H. Khashan, “On Weakly S-Primary Ideals of Commutative Rings”, Preprints, 2021, 2021090486. https://doi.org/10.20944/preprints202109.0486.v1
F. Farzalipour and P. Ghiasvand, “On the union of graded prime submodules”, Thai journal of mathematics, vol. 9, no. 1, pp. 49-55, 2012. [On line]. Available: https://bit.ly/3E05YLm
E. Massaoud, “S-primary ideals of a commutative ring”, Communications in Algebra, vol. 50, no. 3, pp. 988-997, 2022. https://doi.org/10.1080/00927872.2021.1977939
C. Nastasescu and F. Van Oystaeyen, Methods of graded rings. Berlin: Springer, 2004.
M. Refai, “Graded radicals and graded prime spectra”, Far East journal of mathematical sciences, pp. 59-73, 2000.
M. Refai and R. Abu-Dawwas, “On generalizations of graded second submodules” Proyecciones (Antofagasta), vol. 39, no. 6, pp. 1537–1554, 2020. https://doi.org/10.22199/issn.0717-6279-2020-06-0092
M. Refai and K. Al-Zoubi, “On graded primary ideals”, Turkish journal of mathematics, vol. 28, no. 3, pp. 217-229, 2004. [On line]. Available: https://bit.ly/3NA382Q
H. Saber, T. Alraqad and R. Abu-Dawwas, “On graded s-prime submodules”, arXiv: 2008.05529 2020.
H. Saber, T. Alraqad, R. Abu-Dawwas, H. Shtayat and M. Hamdan, “On graded weakly S-prime ideals”, Preprints, 2021. https://doi.org/10.20944/preprints202108.0479.v1
R. N. Uregen, U. Tekir, K.P. Shum and S. Koc, “On graded 2-absorbing quasi primary ideals”, Southeast Asian Bulletin of Mathematics, vol. 43, no. 4, pp. 601-613, 2019. [On line]. Available: https://bit.ly/3NzdSij
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Copyright (c) 2022 Tamem Al-shorman, Malik Bataineh, Rashid Abu-dawwas
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