Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON GRADED J-IDEALS OVER GRADED RINGS

  • Tamem Al-Shorman (Department of Mathematics and Statistics Jordan University of Science and Technology) ;
  • Malik Bataineh (Department of Mathematics and Statistics Jordan University of Science and Technology) ;
  • Ece Yetkin Celikel (Department of Basic Sciences Faculty of Engineering Hasan Kalyoncu University)
  • Received : 2022.06.07
  • Accepted : 2022.12.22
  • Published : 2023.04.30
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Abstract

The goal of this article is to present the graded J-ideals of G-graded rings which are extensions of J-ideals of commutative rings. A graded ideal P of a G-graded ring R is a graded J-ideal if whenever x, y ∈ h(R), if xy ∈ P and x ∉ J(R), then y ∈ P, where h(R) and J(R) denote the set of all homogeneous elements and the Jacobson radical of R, respectively. Several characterizations and properties with supporting examples of the concept of graded J-ideals of graded rings are investigated.

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References

  1. R. Abu-Dawwas and M. Bataineh, Graded r-ideals, Iran. J. Math. Sci. Inform. 14 (2019), no. 2, 1-8.
  2. T. Al-Shorman and M. Bataineh, On graded classical S-primary submodules, arXiv preprint arXiv:2204.07578 (2022).
  3. T. Al-Shorman, M. Bataineh, and R. Abu-Dawwas, Generalizations of graded S-primary ideals, Proyecciones 41 (2022), 1353-1376. https://doi.org/10.22199/issn.0717-6279-5357
  4. K. Al-Zoubi and M. Al-Azaizeh, On graded classical 2-absorbing second submodules of graded modules over graded commutative rings, Afr. Mat. 33 (2022), no. 2, Paper No. 43, 10 pp. https://doi.org/10.1007/s13370-022-00982-1
  5. K. Al-Zoubi, F. Al-Turman, and E. Y. Celikel, gr-n-ideals in graded commutative rings, Acta Univ. Sapientiae Math. 11 (2019), no. 1, 18-28. https://doi.org/10.2478/ausm2019-0002
  6. W. T. Ashby, On graded principal ideal domains, JP J. Algebra Number Theory Appl. 24 (2012), no. 2, 159-171.
  7. M. Atiyah, Introduction to Commutative Algebra, CRC Press, 2018.
  8. F. Farzalipour and P. Ghiasvand, On the union of graded prime submodules, Thai J. Math. 9 (2011), no. 1, 49-55.
  9. A. V. Kelarev, On the Jacobson radical of graded rings, Comment. Math. Univ. Carolin. 33 (1992), no. 1, 21-24.
  10. H. A. Khashan and A. B. Bani-Ata, J-ideals of commutative rings, Int. Electron. J. Algebra 29 (2021), 148-164. https://doi.org/10.24330/ieja.852139
  11. C. Nastasescu and F. Van Oystaeyen, Methods of graded rings, Lecture Notes in Mathematics, 1836, Springer-Verlag, Berlin, 2004. https://doi.org/10.1007/b94904
  12. K. H. Oral, Tekir, and A. G. Agargun, On graded prime and primary submodules, Turkish J. Math. 35 (2011), no. 2, 159-167.
  13. M. Refai and R. Abu-Dawwas, On generalizations of graded second submodules, Proyecciones 39 (2020), no. 6, 1537-1554. https://doi.org/10.22199/issn.0717-6279-2020-06-0092
  14. M. Refai and K. Al-Zoubi, On graded primary ideals, Turkish J. Math. 28 (2004), no. 3, 217-229.
  15. M. Refai, M. Hailat, and S. Obiedat, Graded radicals and graded prime spectra, Far East J. Math. Sci. (FJMS) 2000, Special Volume, Part I, 59-73.
  16. H. Saber, T. Alraqad, and R. Abu-Dawwas, On graded s-prime submodules, AIMS Math. 6 (2021), no. 3, 2510-2524. https://doi.org/10.3934/math.2021152