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Some Properties of Dedekind Modules and Q-modules

  • Motmaen, Shahram (Department of Mathematics and Applications, Univeristy of Mohaghegh Ardabili) ;
  • Darani, Ahmad Yousefian (Department of Mathematics and Applications, Univeristy of Mohaghegh Ardabili) ;
  • Rahmatinia, Mahdi (Department of Mathematics and Applications, Univeristy of Mohaghegh Ardabili)
  • Received : 2016.03.23
  • Accepted : 2017.02.04
  • Published : 2018.09.23

Abstract

A Q-module is a module in which every nonzero submodule of M is a finite product of primary submodules of M. This paper is devoted to study some properties of Dedekind modules and Q-modules.

Keywords

Dedekind module;multiplication module;invertible submodule;Q-module

References

  1. M. M. Ali, Some remarks on generalized GCD domains, Comm. Algebra, 36(2008), 142-164.
  2. M. M. Ali, Idempotent and nilpotent submodules of multiplication modules, Comm. Algebra, 36(2008), 4620-4642. https://doi.org/10.1080/00927870802186805
  3. M. M. Ali, Invertibility of multiplication modules II, New Zealand J. Math., 39(2009), 45-64.
  4. M. M. Ali, Invertibility of multiplication modules III, New Zealand J. Math., 39 (2009), 193-213.
  5. R. Ameri, On the prime submodules of multiplication modules, Int. J. Math. Math. Sci., 27(2003), 1715-1724.
  6. D. D. Anderson, Noetherian rings in which every ideal is a product of primary ideals, Canad. Math. Bull., 23(1980), 457-459. https://doi.org/10.4153/CMB-1980-068-2
  7. D. D. Anderson and L. A. Mahaney, Commutative rings in which every ideal is a product of primary ideals, J. Algebra, 106(1987), 528-535. https://doi.org/10.1016/0021-8693(87)90014-7
  8. A. Barnard, Multiplication modules, J. Algebra, 71(1981), 174-178.
  9. Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(1998), 755-799.
  10. T. W. Hungerford, Algebra, Springer-Verlag (1974).
  11. A. G. Naoum and F. H. Al-Alwan, Dedekind modules, Comm. Algebra, 24(2)(1996), 397-412. https://doi.org/10.1080/00927879608825576
  12. R. Y. Sharp, Steps in Commutative Algebra, Cambridge University Press, (1990).
  13. P. F. Smith, Some remarks on multiplication modules, Arch. Math., 50(1988), 223-235. https://doi.org/10.1007/BF01187738