Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

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)
  • Received : 2018.08.03
  • Accepted : 2019.05.02
  • Published : 2019.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  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