ON GRADED STRONGLY 1-ABSORBING PRIMARY IDEALS AND GRADED 2-ABSORBING I-PRIMARY IDEALS

Maria Asa Pitayani

doi:10.22146/jmt.107056

ON GRADED STRONGLY 1-ABSORBING PRIMARY IDEALS AND GRADED 2-ABSORBING I-PRIMARY IDEALS

https://doi.org/10.22146/jmt.107056

Maria Asa Pitayani^(1*)

(1) Universitas Gadjah Mada
(*) Corresponding Author

Abstract

Given a group G with identity element e and a G-graded commutative ring R with unity 1. This paper introduces a new concept, namely, graded strongly 1-absorbing primary ideals, which is a subclass of the graded 1-absorbing primary ideals. A proper graded ideal I of R is said to be a graded strongly 1-absorbing primary ideal of R if whenever non-unit elements a,b, and c belong to h(R) with abc in I, then either ab is in I or c belongs to Grad({0}). Several properties of graded strongly 1-absorbing primary ideals will be investigated in this paper. Furthermore, a new structure called graded 2-absorbing I-primary ideal is also introduced.

Keywords

Graded 1-Absorbing Primary Ideal; Graded Strongly 1-Absorbing Primary Ideal, Graded 2-Absorbing I-Primary Ideal.

Full Text:

PDF

References

Farzalipour, F., & Ghiasvand, P. (2011). On the union of graded prime submodules. Thai Journal of Mathematics, 9(1), 49–55.

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

Refai, M., & Al-Zoubi, K. (2004). On graded primary ideals. Turkish Journal of Mathematics, 28(3), 217–230.

Al-Zoubi, K., & Sharafat, N. (2017). On graded 2-absorbing primary and graded weakly 2-absorbing primary ideals. Journal of the Korean Mathematical Society, 54(2), 675–684.

Abu-Dawwas, R., & Bataineh, M. (2022). Graded 1-absorbing primary ideals. In Turkish Journal of Mathematics – Studies on Scientific Developments in Geometry, Algebra, and Applied Mathematics, Istanbul, Turkey, Feb. 1–3, 2022.

Călugăreanu, G. (2015). UN-rings. Journal of Algebra and Its Applications, 15, 1650182.

Alshehry, A. S., Abu-Dawwas, R., & Al-Rashdan, M. (2023). Some notes on graded weakly 1-absorbing primary ideals. Demonstratio Mathematica, 56(1), 20230111.

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

Almahdi, F. A. A., Bouba, E. M., & Koam, A. N. A. (2020). On strongly 1-absorbing primary ideals of commutative rings. Bulletin of the Korean Mathematical Society, 57(5), 1205–1213.

Badawi, A., & Celikel, E. Y. (2020). On 1-absorbing primary ideals of commutative rings. Journal of Algebra and Its Applications, 19(6).

Akray, I., Jabbar, A. K., & Othman, S. A. (2024). Graded n-absorbing I-ideals. Palestine Journal of Mathematics, 13(1).

DOI: https://doi.org/10.22146/jmt.107056