Some properties of graded generalized 2-absorbing submodules

• Autorzy: Alghueiri, Shatha , Al-Zoubi, Khaldoun
• Języki publikacji: EN

Abstrakty

EN

Let G be an abelian group with identity e . Let R be a G -graded commutative ring and M a graded R -module. In this paper, we will obtain some results concerning the graded generalized 2-absorbing submodules and their homogeneous components. Special attention has been paid, when graded rings are graded gr-Noetherian, to find extra properties of these graded submodules.

Słowa kluczowe

PL

algebra homologiczna; teoria modułów; podmoduły

EN

graded generalized 2-absorbing submodule; graded 2-absorbing submodule; graded 2-absorbing primary submodule

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 343--353
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Alghueiri, Shatha

• Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan,

autor

Al-Zoubi, Khaldoun

• Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan,

Bibliografia

• [1] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), 417–429.
• [2] A.Y. Darani and F. Soheilnia, 2-absorbing and weakly 2-absorbing submoduels, Thai J. Math. 9 (2011), no. 3, 577–584.
• [3] Sh. Payrovi and S. Babaei, On 2-absorbing submodules, Algebra Collq. 19 (2012), 913–920, DOI: https://doi.org/10.1142/S1005386712000776.
• [4] F. Farshadifar and H. Ansari-Toroghy, Generalized 2-absorbing submodules, An. Stiint. Univ. Ovidius Constanta Ser. Mat. 28 (2020), no. 1, 99–109.
• [5] M. Refai and K. Al-Zoubi, On graded primary ideals, Turk. J. Math. 28 (2004), no. 3, 217–229.
• [6] K. Al-Zoubi, R. Abu-Dawwas, and S. Çeken, On graded 2-absorbing and graded weakly 2-absorbing ideals, Hacet. J. Math. Stat. 48 (2019), no. 3, 724–731, DOI: https://doi.org/10.15672/HJMS.2018.543.
• [7] K. Al-Zoubi and N. Sharafat, On graded 2-absorbing primary and graded weakly 2-absorbing primary ideals, J. Korean Math. Soc. 54 (2017), no. 2, 675–684, DOI: https://doi.org/10.4134/JKMS.j160234.
• [8] K. Al-Zoubi and R. Abu-Dawwas, On graded 2-absorbing and weakly graded 2-absorbing submodules, J. Math. Sci. Adv. Appl. 28 (2014), 45–60.
• [9] K. Al-Zoubi and M. Al-Azaizeh, Some properties of graded 2-absorbing and graded weakly 2-absorbing submodules, J. Nonlinear Sci. Appl. 12 (2019), no. 8, 503–508.
• [10] K. Al-Zoubi, I. Al-Ayyoub, and M. Al-Dolat, On graded 2-absorbing compactly packed modules, Adv. Stud. Contemp. Math. (Kyungshang). 28 (2018), no. 3, 479–486.
• [11] R. Abu-Dawwas, M. Bataineh, and H. Shashan, Graded generalized 2-absorbing submodules, Beitr. Algebra Geom. 62 (2021), no. 4, 883–891, DOI: https://doi.org/10.1007/s13366-020-00544-1.
• [12] R. Hazrat, Graded Rings and Graded Grothendieck Groups, Cambridge University Press, Cambridge, 2016.
• [13] C. Nastasescu and F. Van Oystaeyen, Graded and filtered rings and modules, Lecture Notes in Mathematics 758, Springer-Verlag, Berlin-New York, 1982.
• [14] C. Nastasescu and F. Van Oystaeyen, Graded Ring Theory, Mathematical Library 28, North-Holland Pub. Co., Amsterdam, 1982.
• [15] C. Nastasescu and F. Van Oystaeyen, Methods of Graded Rings, LNM 1836, Springer-Verlag, Berlin-Heidelberg, 2004.
• [16] S.E. Atani and F. Farzalipour, On graded secondary modules, Turk. J. Math. 31 (2007), no. 4, 371–378.
• [17] J. Escoriza and B. Torrecillas, Multiplication rings and graded rings, Comm. Algebra 27 (1999), no. 12, 6213–6232.
• [18] K. Al-Zoubi and A. Al-Qderat, Some properties of graded comultiplication modules, Open Math. 15 (2017), no. 1, 187–192, DOI: https://doi.org/10.1515/math-2017-0016.
• [19] F. Farzalipour and P. Ghiasvand, On the union of graded prime submodules, Thai. J. Math. 9 (2011), no. 1, 49–55.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).

Identyfikatory

DOI

10.1515/dema-2022-0017