DOI QR코드

DOI QR Code

ON PRIME SUBMODULES OF AN INJECTIVE MODULE OVER A NOETHERIAN RING

  • Pourshafiey, Zahra (Department of Mathematics, Shahid Bahonar University of Kerman) ;
  • Nekooei, Reza (Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman)
  • Received : 2017.10.10
  • Accepted : 2018.04.09
  • Published : 2018.06.25

Abstract

In this paper, we characterize the prime submodules of an injective module over a Noetherian ring.

Keywords

References

  1. W. Bruns and J. Herzog , Cohen-Macaulay rings, Revised edition, Cambridge University, 1998.
  2. S. Hedayat and R. Nekooei, Characterization of prime submodules of a finitely generated free module over a PID, Houston J. Math. 1(31) (2005), 75-85.
  3. S. Hedayat and R. Nekooei, Prime and radical submodules of free modules over a PID, Houston J. Math. 2 (32) (2006), 355-367.
  4. H. Kim, Module-theoretic characterizations of t-linkative domains, Comm. Alg. 5(36), (2008), 1649-1670.
  5. C. P. Lu, Prime submodules of modules, Comment. Math. Univ. Sancti Pauli. 33(1) (1984), 61-69.
  6. R. L. McCasland and M. E. Moore, Prime submodules, Comm. Alg. 20(6) (1992), 1803-1817. https://doi.org/10.1080/00927879208824432
  7. F. Mirzaei and R. Nekooei, On prime submodules of a free module of finite rank over a commutative ring, Comm. Alg. 44 (2016), 3966-3975. https://doi.org/10.1080/00927872.2015.1090576
  8. F. Mirzaei and R. Nekooei, Characterization of prime submodules of a free module of finite rank over a valuation domain, J. Korean Math. Soc 54(1) (2017), 59-68. https://doi.org/10.4134/JKMS.j150591
  9. Y. Tiras and A. Harmanci and P.F. Smith, A Characterization of Prime Submodule, J. Alg. 212(2) (1999), 743-752. https://doi.org/10.1006/jabr.1998.7636