Abstract
Let G be a group, R a G-graded commutative ring with nonzero unity, and M a G-graded R-module. In this article, we introduce the concept of graded generalized 2-absorbing submodules as a generalization of graded 2-absorbing submodules, and investigate some properties of this new class of graded submodules. A proper graded R-submodule N of M is said to be a graded generalized 2-absorbing R-submodule of M if whenever x and y are homogeneous elements of R and m is a homogeneous element of M such that \(xym\in N\), then either it is the case that x or y is in the graded radical of \((N:_{R} m)\), or \(xy\in (N:_{R} M)\).
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References
Abu-Dawwas, R.: Multiplication components of graded modules. Ital. J. Pure Appl. Math. 35, 389–392 (2015)
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)
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)
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)
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)
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)
Atani, S.E.: On graded prime submodules. Chiang Mai J. Sci. 33(1), 3–7 (2006)
Celikel, E.Y.: On graded \(2\)-absorbing primary submodules. Int. J. Pure Appl. Math. 109(4), 869–879 (2016)
Escoriza, J., Torrecillas, B.: Multiplication objects in commutative Grothendieck category. Commun. Algebra 26, 1867–1883 (1998)
Farshadifar, F., Ansari-Toroghy, H.: Generalized \(2\)-absorbing submodules. Analele Stiintifice ale Universitatii Ovidius Constanta 28(1), 99–109 (2020)
Farzalipour, F., Ghiasvand, P.: On the union of graded prime submodules. Thai J. Math. 9(1), 49–55 (2011)
Khaksari, K., Jahromi, F.R.: Multiplication graded modules. Int. J. Algebra 7(1), 17–24 (2013)
Nastasescu, C., van Oystaeyen, F.: Methods of graded rings. Lecture Notes in Mathematics, vol. 1836. Springer, Berlin (2004)
Soheilnia, F., Darani, A.Y.: On graded 2-absorbing and graded weakly 2-absorbing primary ideals. Kyungpook Math. J. 57(4), 559–580 (2017)
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Abu-Dawwas, R., Bataineh, M. & Shashan, H. Graded generalized 2-absorbing submodules. Beitr Algebra Geom 62, 883–891 (2021). https://doi.org/10.1007/s13366-020-00544-1
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DOI: https://doi.org/10.1007/s13366-020-00544-1