대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제34권3호
  • /
  • Pages.729-741
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  • 2019
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON PRIME SUBMODULES OF A FINITELY GENERATED PROJECTIVE MODULE OVER A COMMUTATIVE RING

  • Nekooei, Reza (Department of Pure Mathematics Faculty of Mathematics and Computer Shahid Bahonar University of Kerman) ;
  • Pourshafiey, Zahra (Faculty of Mathematics and Computer Shahid Bahonar University of Kerman)
  • 투고 : 2018.08.03
  • 심사 : 2019.05.02
  • 발행 : 2019.07.31
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초록

In this paper we give a full characterization of prime submodules of a finitely generated projective module M over a commutative ring R with identity. Also we study the existence of primary decomposition of a submodule of a finitely generated projective module and characterize the minimal primary decomposition of this submodule. Finally, we characterize the radical of an arbitrary submodule of a finitely generated projective module M and study submodules of M which satisfy the radical formula.

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참고문헌

  1. M. Alkan and Y. Tiras, Projective modules and prime submodules, Czechoslovak Math. J. 56(131) (2006), no. 2, 601-611. https://doi.org/10.1007/s10587-006-0041-5
  2. S. Hedayat and R. Nekooei, Characterization of prime submodules of a finitely generated free module over a PID, Houston J. Math. 31 (2005), no. 1, 75-85.
  3. S. Hedayat and R. Nekooei, Primary decomposition of submodules of a finitely generated module over a PID, Houston J. Math. 32 (2006), no. 2, 369-377.
  4. T. W. Hungerford, Algebra, Graduate Texts in Mathematics, 73, Springer-Verlag, New York, 1980.
  5. F. Mirzaei and R. Nekooei, On prime submodules of a finitely generated free module over a commutative ring, Comm. Algebra 44 (2016), no. 9, 3966-3975. https://doi.org/10.1080/00927872.2015.1090576
  6. F. Mirzaei and R. Nekooei, On radical formula and Prufer domains, Bull. Iranian Math. Soc. 42 (2016), no. 3, 555-563.
  7. D. Pusat-Yilmaz and P. F. Smith, Radicals of submodules of free modules, Comm. Algebra 27 (1999), no. 5, 2253-2266. https://doi.org/10.1080/00927879908826563