Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

GRADED UNIFORMLY pr-IDEALS

  • Received : 2020.03.03
  • Accepted : 2020.06.04
  • Published : 2021.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

Let R be a G-graded commutative ring with a nonzero unity and P be a proper graded ideal of R. Then P is said to be a graded uniformly pr-ideal of R if there exists n ∈ ℕ such that whenever a, b ∈ h(R) with ab ∈ P and Ann(a) = {0}, then bn ∈ P. The smallest such n is called the order of P and is denoted by ordR(P). In this article, we study the characterizations on this new class of graded ideals, and investigate the behaviour of graded uniformly pr-ideals in graded factor rings and in direct product of graded rings.

Keywords

References

  1. R. Abu-Dawwas, Graded semiprime and graded weakly semiprime ideals, Ital. J. Pure Appl. Math. No. 36 (2016), 535-542.
  2. R. Abu-Dawwas, On graded semi-prime rings, Proc. Jangjeon Math. Soc. 20 (2017), no. 1, 19-22.
  3. R. Abu-Dawwas and M. Bataineh, Graded r-ideals, Iran. J. Math. Sci. Inform. 14 (2019), no. 2, 1-8. https://doi.org/10.14492/hokmj/1562810507
  4. K. Al-Zoubi, R. Abu-Dawwas, and S. Ceken, On graded 2-absorbing and graded weakly 2-absorbing ideals, Hacet. J. Math. Stat. 48 (2019), no. 3, 724-731. https://doi.org/10.15672/hjms.2018.543
  5. K. Al-Zoubi and M. Al-Dolat, On graded classical primary submodules, Adv. Pure Appl. Math. 7 (2016), no. 2, 93-96. https://doi.org/10.1515/apam-2015-0021
  6. M. Bataineh and R. Abu-Dawwas, Graded almost 2-absorbing structures, JP J. Algebra, Number Theory Appl. 39 (2017), no. 1, 63-75.
  7. R. Gilmer, Multiplicative Ideal Theory, Marcel Dekker, Inc., New York, 1972.
  8. 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
  9. D. G. Northcott, Lessons on Rings, Modules and Multiplicities, Cambridge University Press, London, 1968.
  10. M. Refai and K. Al-Zoubi, On graded primary ideals, Turkish J. Math. 28 (2004), no. 3, 217-229.
  11. M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), no. 1, 14-17. http://projecteuclid.org/euclid.pja/1195510144 https://doi.org/10.3792/pjaa.73.14