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On Divisorial Submodules

  • DARANI, AHMAD YOUSEFIAN (Department of Mathematics and Applications, University of Mohaghegh Ardabili) ;
  • RAHMATINIA, MAHDI (Department of Mathematics and Applications, University of Mohaghegh Ardabili)
  • Received : 2014.08.22
  • Accepted : 2015.05.13
  • Published : 2015.12.23

Abstract

This paper is devoted to study the divisorial submodules. We get some equivalent conditions for a submodule to be a divisorial submodule. Also we get equivalent conditions for $(N{\cap}L)^{-1}$ to be a ring, where N, L are submodules of a module M.

Keywords

References

  1. M. M. Ali, Invertibility of multiplication modules, New Zealand J. Math., 35(2006), 17-29.
  2. M. M. Ali, Invertibility of multiplication modules II, New Zealand J. Math., 39(2009), 45-64.
  3. M. M. Ali, Some remarks on generalized GCD domains, Comm. Algebra, 36(2008), 142-164. https://doi.org/10.1080/00927870701665271
  4. M. M. Ali, Invertibility of multiplication modules III, New Zealand J. Math., 39(2009), 139-213. https://doi.org/10.1080/03014220909510567
  5. M. M. Ali, Idempotent and nilpotent submodules of multiplication modules, Comm. Algebra, 36(2008), 4620-4642. https://doi.org/10.1080/00927870802186805
  6. M. M. Ali, The transform formula for submodules of multiplication modules, New Zealand J. Math., 41(2011), 25-37.
  7. R. Ameri, On the prime submodules of multiplication modules, Internat. J. Math. Math. Sci., 27(2003), 1715-1724.
  8. A. Barnard, Multiplication modules, J. Algebra, 71(1981), 174-178. https://doi.org/10.1016/0021-8693(81)90112-5
  9. Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(1998), 755-799.
  10. E. Houston, S. Kabbaj, T. Lucas and A. Mimouni When is the dual of an ideal a ring?, J. Algebra, 225(2000), 429-450. https://doi.org/10.1006/jabr.1999.8142
  11. M. Fontana, J. Hukaba and I. Papick, Prufer Domains, Marcel Dekker, (1997).
  12. R. Gilmer, Multiplicative ideal theory, Marcel Dekker: New York, (1972).
  13. M. D. Larsen and P. J. MacCaarthy, Multiplication theory of ideal, Academic Press: New York, (1971).
  14. A. G. Naoum, Flat modules and multiolication modules, Periodica. Math. Hungar., 21(1990), 309-317. https://doi.org/10.1007/BF02352695
  15. A. G. Naoum and F. H. Al-Alwan, Dedekind modules, Comm. Algebra, 24(1996), 225-230.
  16. P. F. Smith, Multiplication modules, Comm. Algebra, 16(1988), 755-799. https://doi.org/10.1080/00927878808823601
  17. P. F. Smith, Some remarks on multiplication modules, Arch. der. Math., 50(1988), 223-235. https://doi.org/10.1007/BF01187738