Volume 25 • Issue 4 • PP: 73-79 • 2025
On Gr-2-nil ideals of graded commutative rings
View PDF Abstract
Let G be a group with identity e and let W be a G-graded ring. In this paper, we introduce and study the concept of Gr-2-nil ideals of W. We obtain many results concerning gr-2-nil ideals. Some characterizations of gr-2-nil ideals and their homogeneous components are given. A proper graded ideal I of W is said to be a gr-2-nil ideal of W if whenever rg, sh, ti ∈ h(W) with rgshti ∈ I, then either rgsh ∈ Gr (0) or rgti ∈ I or shti ∈ I.
Keywords
References
[1] R.Abu-Dawwas, On graded strongly 1-absorbing primary ideals, Khayyam Journal of Mathematics, 8 (1) (2022), 42–52.
[2] K. Al-Zoubi, R. Abu-Dawwas, and S. Ceken, On graded 2-absorbing and graded weakly 2-absorbing ideals, Hacettepe Journal of Mathematics and Statistics, 48 (3) (2019), 724-731.
[3] K. Al-Zoubi and F. Al-TURMAN and Ece Yetkin Celikel, gr-n-ideals in graded commutative rings, Acta Univ. Sapientiae, Mathematica, 11 (1) (2019), 18-28.
[4] K. Al-Zoubi, S. Alghueiri and Ece Yetkin Celikel, gr-(2,n)-ideals in graded commutative rings, Commentationes Mathematicae Universitatis Carolinae, 61 (2) (2020), 129-138.
[5] K. Al-Zoubi, N. sharafat, On graded 2-absorbing primary and graded weakly 2-absorbing primary ideals, J. Korean Math. Soc., 54 (2) ( 2017) , 675-684.
[6] S.E. Atani, On graded weakly prime ideals. Turk. J. Math. 30 (4), 351-358, 2006.
[7] R. Hazrat, Graded Rings and Graded Grothendieck Groups. Cambridge University Press, Cambridge (2016)
[8] C. Nastasescu and F. Van Oystaeyen, Graded and filtered rings and modules, Lecture notes in mathematics 758, Berlin-New York: Springer-Verlag, 1982.
[9] C. Nastasescu, F. Van Oystaeyen, Graded Ring Theory, Mathematical Library 28, North Holand, Amsterdam, 1982.
[10] C. Nastasescu and F. Van Oystaeyen, Methods of Graded Rings, LNM 1836. Berlin-Heidelberg: Springer-Verlag, 2004.
[11] M. Refai and K. Al-Zoubi, On graded primary ideals, Turkish J. Math. 28(3) (2004), 217–229.
[12] M. Refai, M. Hailat and S. Obiedat, Graded radicals and graded prime spectra, Far East Journal of Mathematical Sciences, part I, 59-73, (2000).
[13] F. Soheilnia and A. Y. Darani, On Graded 2-Absorbing and Graded Weakly 2-Absorbing Primary Ideals, Kyungpook Math. J., 57(4) (2017), 559-580.
Cite This Article
Choose your preferred format