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Graded I-second submodules

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EN
Abstrakty
EN
Let G be a group with identity e, R be a G-graded commutative ring with a nonzero unity 1, I be a graded ideal of R, and M be a G-graded R-module. In this article, we introduce the concept of graded I-second submodules of M as a generalization of graded second submodules of M and achieve some relevant outcomes.
Wydawca
Rocznik
Strony
1--8
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
  • Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan
  • Department of Mathematics, Yarmouk University, Irbid, Jordan
Bibliografia
  • [1] M. Refai, M. Hailat and S. Obiedat, Graded radicals and graded prime spectra, Far East J. Math. Sci. 1(2000), 59-73.
  • [2] S. E. Atani, On graded prime submodules, Chiang Mai J. Sci. 33(2006), no. 1, 3-7.
  • [3] R. Abu-Dawwas and K. Al-Zoubi, On graded weakly classical prime submodules, Iran. J. Math. Sci. Inform. 12(2017), no. 1, 153-161.
  • [4] R. Abu-Dawwas, K. Al-Zoubi and M. Bataineh, Prime submodules of graded modules, Proyecciones 31(2012), no. 4, 355-361.
  • [5] K. Al-Zoubi and R. Abu-Dawwas, On graded quasi-prime submodules, Kyungpook Math. J. 55(2015), 259-266.
  • [6] K. Al-Zoubi, M. Jaradat and R. Abu-Dawwas, On graded classical prime and graded prime submodules, Bull. Iranian Math. Soc. 41(2015), no. 1, 205-2013.
  • [7] S. E. Atani, On graded weakly prime ideals, Turkish J. Math. 30(2006), 351-358.
  • [8] S. E. Atani, On graded weakly prime submodules, Int. Math. Forum 1(2006), no. 2, 61-66.
  • [9] C. Nastasescu and F. van Oystaeyen, Methods of Graded Rings, Lecture Notes in Mathematics, 1836, Springer-Verlag, Berlin, 2004.
  • [10] H. Ansari-Toroghy and F. Farshadifar, On graded second modules, Tamkang J. Math. 43(2012), no. 4, 499-505.
  • [11] S. Çeken and M. Alkan, On graded second and coprimary modules and graded second representations, Bull. Malaysian Math. Sci. Soc. Ser. 238(2015), no. 4, 1317-1330.
  • [12] S. E. Atani and F. Farzalipour, On graded secondary modules, Turkish J. Math. 31(2007), 371-378.
  • [13] F. Farshadifar and H. Ansari-Toroghy, I-second submodules of a module, Matematicki Vesnik 72(2020), no. 1, 58-65.
  • [14] I. Akray, I-prime ideals, J. Algebra Relat. Topics 4(2016), no. 2, 41-47.
  • [15] F. Farzalipour and P. Ghiasvand, On the union of graded prime submodules, Thai J. Math. 9(2011), no. 1, 49-55.
  • [16] D. Northcott, Lessons on Rings, Modules, and Multiplicities, Cambridge University Press, Cambridge, 1968.
  • [17] J. Chen and Y. Kim, Graded irreducible modules are irreducible, Comm. Algebra 45(2017), no. 5, 1907-1913.
  • [18] H. Ansari-Toroghy and F. Farshadifar, Graded comultiplication modules, Chiang Mai J. Sci. 38(2011), no. 3, 311-320.
  • [19] R. Abu-Dawwas and M. Ali, Comultiplication modules over strongly graded rings, Int. J. Pure Appl. Math. 81(2012), no. 5, 693-699.
  • [20] R. Abu-Dawwas, M. Bataineh and A. Dakeek, Graded weak comultiplication modules, Hokkaido Math. J. 48(2019), 253-261.
  • [21] M. Refai and K. Al-Zoubi, On graded primary ideals, Turkish J. Math. 28(2004), no. 3, 217-229.
  • [22] K. H. Oral, Ü. Tekir and A. G. Agargün, On graded prime and primary submodules, Turkish J. Math. 35(2011), 159-167.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8d415ee1-4bd9-474e-bc5f-3395beb6d4a6
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