On graded G2-absorbing and graded strongly G2-absorbing second submodules
Keywords:graded generalized 2-absorbing second submodule, graded 2-absorbing submodule, graded 2-absorbing second submodule
In this paper, we introduce the concepts of graded G2-absorbing and graded strongly G2-absorbing second submodules of graded modules over graded commutative rings. We give a number of results concerning these classes of graded submodules and their homogeneous components.
K. Al-Zoubi and M. Al-Azaizeh, “On Graded 2-absorbing second submodules of graded modules over graded commutative rings”, Kragujevac Journal of Mathematics, vol. 48, no. 1, pp. 55-66, 2024.
K. Al-Zoubi and A. Al-Qderat, “Some properties of graded comultiplication modules”, Open Mathematics, vol. 15, pp. 187-192, 2017. https://doi.org/10.1515/math-2017-0016
K. Al-Zoubi, R. Abu-Dawwas and S. Çeken, “On graded 2-absorbing and graded weakly 2-absorbing ideals”, Hacettepe Journal of Mathematics & Statistics, vol. 48, no. 3, pp. 724-731, 2019.
K. Al-Zoubi and R. Abu-Dawwas, “On graded 2-absorbing and weakly graded 2-absorbing submodules”, Journal of Mathematical Sciences: Advances and Applications, vol. 28, pp. 45-60, 2014.
K. Al-Zoubi and N. Sharafat, “On graded 2-absorbing primary and graded weakly 2-absorbing primary ideals”, Journal of the Korean Mathematical Society, vol. 54, no. 2, pp. 675-684, 2017. https://doi.org/10.4134/JKMS.j160234
S. Alghueiri and K. Al-Zoubi, “Some properties of graded generalized 2-absorbing submodules”, Demonstratio Mathematica, vol. 55, pp. 343-353, 2022. https://doi.org/10.1515/dema-2022-0017
H. Ansari-Toroghy and F. Farshadifar, Graded comultiplication modules, Chiang Mai Journal of Science , vol. 38, no. 3, pp. 311-320, 2011.
H. Ansari-Toroghy and F. Farshadifar, “On graded second modules”, Tamkang Journal of Mathematics, vol. 43, no. 4, pp. 499-505, 2012.
H. Ansari-Toroghy, F. Farshadifar and S. Maleki-Roudposhti, “Generalized 2-absorbing and strongly generalized 2-absorbing second sub-modules”, Algebra and Discrete Mathematics, vol. 29, no. 2, pp. 161-172, 2020. https://doi.org/10.12958/adm585
S. E. Atani, “On graded prime submodules”, Chiang Mai Journal of Science, vol. 33, no. 1, pp. 3-7, 2006.
S. E. Atani and R. E. Atani, Graded multiplication modules and the graded ideal θg(M)”, Turkish Journal of Mathematics, vol. 35, no. 1, pp. 1-9, 2011.
S. E. Atani and F. Farzalipour, “On graded secondary modules”, Turkish Journal of Mathematics, vol. 31, pp. 371-378, 2007.
S. Çeken and M. Alkan, “On graded second and coprimary modules and graded secondary representations”, The Bulletin of the Malaysian Mathematical Society Series 2, vol. 38, no. 4, pp. 1317-1330, 2015.
R. Hazrat, Graded Rings and Graded Grothendieck Groups. Cambridge: Cambridge University Press, 2016.
C. Nastasescu and F. Van Oystaeyen, Graded and filtered rings and modules. Lecture notes in mathematics , vol. 758, Berlin: Springer-Verlag, 1982.
C. Nastasescu, F. Van Oystaeyen, Graded Ring Theory. Mathematical Library 28, North Holand, Amsterdam, 1982.
C. Nastasescu and F. Van Oystaeyen, Methods of Graded Rings. Lecture Notes in Mathematics, vol. 1836. Berlin: Springer-Verlag, 2004.
M. Refai and R. Abu-Dawwas, “On generalizations of graded second submodules”, Proyecciones (Antofagasta), vol. 39, no. 6, pp. 1537-1554, 2020. https://doi.org/10.22199/issn.0717-6279-2020-06-0092
M. Refai and K. Al-Zoubi, “On graded primary ideals”, Turkish Journal of Mathematics, vol. 28, no. 3, pp. 217-229, 2004.
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