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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)
  • Received : 2018.08.03
  • Accepted : 2019.05.02
  • Published : 2019.07.31

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

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