Graded 2r-Ideals


Abstract views: 38 / PDF downloads: 23

Authors

  • Alaa Melhem Department of Mathematics, Faculty of Science, Jadara University, Irbid
  • Rashid Abu-Dawwas
  • Diala Alghazo Yarmouk University

Keywords:

graded r-ideal, graded pr-ideal, graded uniformly pr-ideal

Abstract

Let G be a group and R be a commutative G-graded ring with nonzero unity. In this article, we establish the concept of graded 2r-ideals, which lies somewhere between graded r-ideals and graded uniformly pr-ideals. A proper graded ideal P of R is said to be a graded 2r-ideal of R if whenever x, y ∈ h(R) such that xy ∈ P , then either x2 ∈ P or y ∈ zd(R), where zd(R) is the set of all zero divisors of R. Several properties of graded 2r-ideals have been achieved, and various results have been investigated.

References

R. Abu-Dawwas, On graded strongly 1-absorbing primary ideals, Khayyam Journal of Mathematics, 8 (1) (2022), 42-52.

R. Abu-Dawwas and M. Bataineh, graded r-ideals, Iranian Journal of Mathematical Sciences and Informatics, 14 (2) (2019), 1-8.

R. Abu-Dawwas and M. Refai, Graded uniformly pr-ideals, Bulletin of the Korean Mathematical Society, 58 (1) (2021), 195-204.

K. Alhazmy, F. A. A. Almahdi, E. M. Bouba and M. Tamekkante, On 2r-ideals in commutative rings with zero-divisors, Open Mathematics, 21 (2023), 20220576.

D. D. Anderson and M. Winders, Idealization of a module, Journal of Commutative Algebra, 1 (1) (2009), 3-56.

R. Hazrat, graded rings and graded Grothendieck groups, Cambridge University press, 2016.

C. Nastasescu and F. Oystaeyen, Methods of graded rings, Lecture Notes in Mathematics, 1836, Springer-Verlag, Berlin, 2004.

M. Refai and K. Al-Zoubi, On graded primary ideals, Turkish Journal of Mathematics, 28 (3) (2004), 217-229.

M. Refai, M. Hailat and S. Obiedat, Graded radicals and graded prime spectra, Far East Journal of Mathematical Sciences, (2000), 59-73.

R. N. Uregen, U. Tekir, K. P. Shum and S. Koc, On graded 2-absorbing quasi primary ideals, Southeast Asian Bulletin of Mathematics, 43 (4) (2019), 601-613.

Downloads

Published

2024-11-18

How to Cite

Alaa Melhem, Abu-Dawwas, R. ., & Alghazo, D. (2024). Graded 2r-Ideals. Results in Nonlinear Analysis, 7(4), 64–69. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/469

Most read articles by the same author(s)