대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제37권1호
  • /
  • Pages.1-15
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  • 2022
  • /
  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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DECOMPOSITIONS OF GRADED MAXIMAL SUBMODULES

  • Moh'd, Fida (Department of Basic Sciences Princess Sumaya University for Technology)
  • 투고 : 2020.11.13
  • 심사 : 2021.01.20
  • 발행 : 2022.01.31
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초록

In this paper, we present different decompositions of graded maximal submodules of a graded module. From these decompositions, we derive decompositions of the graded Jacobson radical of a graded module. Using these decompositions, we prove new theorems about graded maximal submodules, improve old theorems, and give other proofs for old theorems.

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참고문헌

  1. E. C. Dade, Group-graded rings and modules, Math. Z. 174 (1980), no. 3, 241-262. https://doi.org/10.1007/BF01161413
  2. S. Ebrahimi Atani and F. Farzalipour, Notes on the graded prime submodules, Int. Math. Forum 1 (2006), no. 37-40, 1871-1880. https://doi.org/10.12988/imf.2006.06162
  3. J. Escoriza and B. Torrecillas, Multiplication objects in commutative Grothendieck categories, Comm. Algebra 26 (1998), no. 6, 1867-1883. https://doi.org/10.1080/00927879808826244
  4. R. Hazrat, Graded rings and graded Grothendieck groups, London Mathematical Society Lecture Note Series, 435, Cambridge University Press, Cambridge, 2016. https://doi.org/10.1017/CBO9781316717134
  5. F. Moh'd amd M. Khader, Graded modules over first strongly graded rings, Malaysian J. Math. Sci. 11 (2017), no. 2, 20520.
  6. C. Nastasescu and F. Van Oystaeyen, Methods of graded rings, Lecture Notes in Mathematics, 1836, Springer-Verlag, Berlin, 2004. https://doi.org/10.1007/b94904
  7. M. Refai and F. A. M. Moh'd, First strongly graded modules, Int. J. Math. Game Theory Algebra 15 (2006), no. 4, 451-457.
  8. M. Refai and F. A. M. Moh'd, More properties on various types of strongly graded rings, Pac.-Asian J. Math. 1 (2007), no. 2, 129-135.
  9. M. Refai and F. A. M. Moh'd, On flexible graded modules, Ital. J. Pure Appl. Math. No. 22 (2007), 125-132.