Graded generalized 2-absorbing submodules. (English) Zbl 1477.13003
Generalized 2-absorbing submodules of a module over a commutative ring were introduced by F. Farshadifar and H. Ansari-Toroghy [An. Ştiinţ. Univ. “Ovidius” Constanţa, Ser. Mat. 28, No. 1, 99–109 (2020; Zbl 1488.13034)]. In this paper, the authors consider the graded version. Several properties of this class of submodules are obtained. It is shown that for a graded multiplication module \(M\), every graded 2-absorbing \(R\)-submodule of \(M\) is grade 2-absorbing primary. Transfer of this property by graded morphism of modules is investigated.
Reviewer: Blas Torrecillas (Almería)
MSC:
| 13A02 | Graded rings |
Keywords:
graded 2-absorbing submodules; graded 2-absorbing primary submodules; graded prime submodulesCitations:
Zbl 1488.13034References:
| [1] | Abu-Dawwas, R., Multiplication components of graded modules, Ital. J. Pure Appl. Math., 35, 389-392 (2015) · Zbl 1330.13002 |
| [2] | Abu-Dawwas, R.; Refai, M., Some remarks on \(R_e\)-multiplication modules over first strongly graded rings, East-West J. Math., 13, 1, 57-61 (2011) · Zbl 1262.13002 |
| [3] | Al-Zoubi, K.; Abu-Dawwas, R., On graded 2-absorbing and weakly graded 2-absorbing submodules, J. Math. Sci. Adv. Appl., 28, 45-60 (2014) · Zbl 1488.16129 |
| [4] | Al-Zoubi, K.; Al-Azaizeh, M., Some properties of graded \(2\)-absorbing and graded weakly \(2\)-absorbing submodules, J. Nonlinear Sci. Appl., 12, 503-508 (2019) · Zbl 1422.13003 · doi:10.22436/jnsa.012.08.01 |
| [5] | Al-Zoubi, K.; Sharafat, N., On graded \(2\)-absorbing primary and graded weakly \(2\)-absorbing primary ideals, J. Korean Math. Soc., 54, 2, 675684 (2017) · Zbl 1358.13002 · doi:10.4134/JKMS.j160234 |
| [6] | Al-Zoubi, K.; Abu-Dawwas, R.; Ceken, S., On graded 2-absorbing and graded weakly 2-absorbing ideals, Hacettepe J. Math. Stat., 48, 3, 724-731 (2019) · Zbl 1488.16129 |
| [7] | Atani, SE, On graded prime submodules, Chiang Mai J. Sci., 33, 1, 3-7 (2006) · Zbl 1099.13001 |
| [8] | Celikel, EY, On graded \(2\)-absorbing primary submodules, Int. J. Pure Appl. Math., 109, 4, 869-879 (2016) · doi:10.12732/ijpam.v109i4.10 |
| [9] | Escoriza, J.; Torrecillas, B., Multiplication objects in commutative Grothendieck category, Commun. Algebra, 26, 1867-1883 (1998) · Zbl 0902.18003 · doi:10.1080/00927879808826244 |
| [10] | Farshadifar, F.; Ansari-Toroghy, H., Generalized \(2\)-absorbing submodules, Analele Stiintifice ale Universitatii Ovidius Constanta, 28, 1, 99-109 (2020) · Zbl 1488.13034 |
| [11] | Farzalipour, F.; Ghiasvand, P., On the union of graded prime submodules, Thai J. Math., 9, 1, 49-55 (2011) · Zbl 1260.13001 |
| [12] | Khaksari, K.; Jahromi, FR, Multiplication graded modules, Int. J. Algebra, 7, 1, 17-24 (2013) · Zbl 1284.13004 · doi:10.12988/ija.2013.13003 |
| [13] | Nastasescu, C.; van Oystaeyen, F., Methods of graded rings (2004), Berlin: Springer, Berlin · Zbl 1043.16017 · doi:10.1007/b94904 |
| [14] | Soheilnia, F.; Darani, AY, On graded 2-absorbing and graded weakly 2-absorbing primary ideals, Kyungpook Math. J., 57, 4, 559-580 (2017) · Zbl 1397.13004 |
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