Citation: Shatha Alghueiri, Khaldoun Al-Zoubi. On graded 2-absorbing $I_{e}$-prime submodules of graded modules over graded commutative rings[J]. AIMS Mathematics, 2020, 5(6): 7624-7631. doi: 10.3934/math.2020487
[1] | K. Al-Zoubi, Some properties of graded 2-prime submodules, Asian-European Journal of Mathematics, 8 (2015), 1550016. |
[2] | K. Al-Zoubi, R. Abu-Dawwas, On graded quasi-prime submodules, Kyungpook Mathematical Journal, 55 (2015), 259-266. |
[3] | K. Al-Zoubi, R. Abu-Dawwas, On graded 2-absorbing and weakly graded 2-absorbing submodules, Journal of mathematical sciences: advances and applications, 28 (2014), 45-60. |
[4] | K. Al-Zoubi, R. Abu-Dawwas, S. Çeken, On graded 2-absorbing and graded weakly 2-absorbing ideals, Hacet. J. Math. Stat., 48 (2019), 724-731. |
[5] | K. Al-Zoubi, M. Al-Azaizeh, On graded classical 2-absorbing submodules of graded modules over graded commutative rings, Rend. Istit. Mat. Univ. Trieste, 50 (2018), 37-46. |
[6] | K. Al-Zoubi, M. Al-Azaizeh, On graded weakly 2-absorbing primary submodules, Vietnam J. Math., 47 (2019), 297-307. |
[7] | K. Al-Zoubi, M. Al-Azaizeh, Some properties of graded 2-absorbing and graded weakly 2- absorbing submodules, J. Nonlinear Sci. Appl., 12 (2019), 503-508. |
[8] | K. Al-Zoubi, I. Al-Ayyoub, M. Al-Dolat, On graded 2-absorbing compactly packed modules, Adv. Stud. Contemp. Math. (Kyungshang), 28 (2018), 479-486. |
[9] | K. Al-Zoubi, A. Al-Qderat, Some properties of graded comultiplication modules, Open Math., 15 (2017), 187-192. |
[10] | K. Al-Zoubi, M. Jaradat, R. Abu-Dawwas, On graded classical prime and graded prime submodules, B. Iran. Math. Soc., 41 (2015), 217-225. |
[11] | K. Al-Zoubi, F. Qarqaz, An Intersection condition for graded prime submodules in Grmultiplication modules, Math. Rep., 20 (2018), 329-336. |
[12] | K. Al-Zoubi, B. Rabab'a, Some properties of graded prime and graded weakly prime submodules, FJMS., 102 (2017), 1613-1624. |
[13] | S. Alghueiri, K. Al-Zoubi, On graded Ie-prime submodules of graded modules over graded commutative rings, Preprint. |
[14] | S. E. Atani, On graded prime submodules, Chiang Mai J. Sci., 33 (2006), 3-7. |
[15] | A. Badawi, On 2-absorbing ideals of commutative rings, B. Aust. Math. Soc., 75 (2007), 417-429. |
[16] | E. Y. Celikel, On graded 2-absorbing primary submodules, International Journal of Pure and Applied Mathematics, 109 (2016), 869-879. |
[17] | A. Y. Darani, F. Soheilnia, 2-absorbing and weakly 2-absorbing submoduels, Thai Journal of Mathematics, 9 (2012), 577-584. |
[18] | F. Farshadifar, 2-absorbing I-prime and 2-absorbing I-second submodules, Algebraic Structures and Their Applications, 6 (2019), 47-55. |
[19] | R. Hazrat, Graded Rings and Graded Grothendieck Groups, Cambridge University Press, 2016. |
[20] | C. Nastasescu, F. Van Oystaeyen, Graded and filtered rings and modules, Springer-Verlag, Berlin Heidelberg, 1979. |
[21] | C. Nastasescu, F. Van Oystaeyen, Graded Ring Theory, Mathematical Library, 1982. |
[22] | C. Nastasescu, F. Van Oystaeyen, Methods of Graded Rings, Springer, 2004. |
[23] | K. H. Oral, Ü. Tekir, A. G. Ağargün, On graded prime and primary submodules, Turk. J. Math., 35 (2011), 159-167. |
[24] | S. Payrovi, S. Babaei, On 2-absorbing submodules, Algebr. Colloq., 19 (2012), 913-920. |
[25] | M. Refai, K. Al-Zoubi, On graded primary ideals, Turk. J. Math., 28 (2004), 217-230. |