TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

CiteScore 2025: 2.7 (Q1)

Powered by:Powered by

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Graded S-r-ideals

, * ,

* Corresponding author · click or hover a name for details

pp. 267–279Vol. 28Issue 1February 2025DOI: 10.47974/JDMSC-2200 Crossmark XML
Received:
08 May 2024
Published Online:
28 Feb 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2200
Pages:
267–279

Abstract

Let G be a group, R be a commutative G-graded ring with nonzero unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R with P ∩ S = ϕ. In this article, we introduce and study the concept of graded S-r-ideals (graded S-pr-ideals). We call P a graded S-r-ideal (graded S-pr-ideal) of R if there exists s ∈ S such that for every homogeneous elements x, y of R with xy ∈ P and Ann(x) = {0}, we have sy ∈ P ((sy)n ∈ P, for some positive integer n). We demonstrate that several properties of graded S-r-ideals (graded S-pr-ideals) are analogous to graded r-ideals (graded pr-ideals).

Keywords

Graded r-idealGraded pr-idealGraded uniformly pr-ideal

Subject Classifications

Primary 13A02Secondary 13A15

References

[1] R. Abu-Dawwas and M. Bataineh, “Graded r-ideals,” Iranian J. Math. Sci. Inform., vol. 14, no. 2, pp. 1-8 (2019).
[2] R. Abu-Dawwas and M. Refai, “Graded uniformly pr-ideals,” Bull. Korean Math. Soc., vol. 58, no. 1, pp. 195-204 (2021).
[3] F. A. A. Almahdi, E. M. Bouba, and M. Tamekkante, “On weakly Sprime ideals of commutative rings,” Analele Univ. “Ovidius” Constanța-Seria Matematica, vol. 29, no. 2, pp. 173-186 (2021).
[4] A. S. Alshehry, “On graded S-primary ideals,” Mathematics, vol. 9, no. 20, pp. 2637 (2021), doi: 10.3390/math9202637.
[5] S. E. Atani, “On graded weakly prime ideals,” Turkish J. Math., vol. 30, pp. 351-358 (2006).
[6] A. Hamed and A. Malek, “S-prime ideals of a commutative ring,” Beitäge zur Algebra und Geometrie/Contributions to Algebra and Geometry, vol. 61, pp. 533-542 (2020).
[7] R. Hazrat, Graded Rings and Graded Grothendieck Groups, Cambridge University Press (2016).
[8] E. Massaoud, “On S-r-ideals and S-pr-ideals of a commutative ring,” Preprint (2022).
[9] E. Massaoud, “S-primary ideals of a commutative ring,” Commun. Algebra (2021), doi: 10.1080/00927872.2021.1977939.
[10] C. Nastasescu and F. Oystaeyen, Methods of Graded Rings, Lecture Notes in Mathematics, vol. 1836, Springer-Verlag, Berlin (2004).
[11] M. Refai and K. Al-Zoubi, “On graded primary ideals,” Turkish J. Math., vol. 28, no. 3, pp. 217-229 (2004).
[12] M. Refai, M. Hailat, and S. Obiedat, “Graded radicals and graded prime spectra,” Far East J. Math. Sci., pp. 59-73 (2000).
[13] H. Saber, T. Alraqad, and R. Abu-Dawwas, “On graded S-prime submodules,” AIMS Math., vol. 6, pp. 2510-2524 (2020).
[14] H. Saber, T. Alraqad, R. Abu-Dawwas, H. Shtayat, and M. Hamdan, “On graded weakly S-prime ideals,” Preprints.org (2021), doi: 10.20944/preprints202108.0479.v1.
[15] R. N. Uregen, U. Tekir, K. P. Shum, and S. Koc, “On graded 2-absorbing quasi-primary ideals,” Southeast Asian Bull. Math., vol. 43, no. 4, pp. 601-613 (2019).

Views: 173Downloads: 74Citations: 0