Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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SOME CHARACTERIZATIONS OF DEDEKIND MODULES

  • Kwon, Tae In (Department of Applied Mathematics Changwon National University) ;
  • Kim, Hwankoo (School of Computer and Information Engineering Hoseo University) ;
  • Kim, Myeong Og (Department of Mathematics Kyungpook National University)
  • Received : 2016.09.30
  • Accepted : 2016.12.16
  • Published : 2017.02.15
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Abstract

In this article, we generalize the concepts of several classes of domains (which are related to a Dedekind domain) to a torsion-free module and it is shown that for a faithful multiplication module over an integral domain, we characterize Dedekind modules, cyclic submodule modules, and discrete valuation modules in terms of factorable modules and a sort of Euclidean algorithm.

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References

  1. M. Ali, Invertibility of multiplication modules, New Zealand J. Math. 35 (2006), 17-29.
  2. M. Alkan, B. Sarac, and Y. Tiras, Dedekind modules, Comm. Algebra 33 (2005), 1617-1626. https://doi.org/10.1081/AGB-200061007
  3. D. F. Anderson, H. Kim, and J. Park, Factorable domains Comm. Algebra 30 (2001), 4113-4120.
  4. Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra 16 (1988), 755-739. https://doi.org/10.1080/00927878808823601
  5. V. Erdogdu, Multiplication modules which are distributive, J. Pure Appl. Algebra 54 (1988), 209-213. https://doi.org/10.1016/0022-4049(88)90031-X
  6. R. Gilmer, Multiplicative Ideal Theory, Queen's University, Kingston Ontario, 1992.
  7. S. C. Lee and R. Varmazyar, Zero-divisor graphs of multiplication modules, Honam Math. J. 34 (2012), 571-584. https://doi.org/10.5831/HMJ.2012.34.4.571
  8. J. Moghaderi and R. Nekooei, Valuation, discrete valuation and Dedekind modules, Intern. Elec. J. Algebra 8 (2010), 18-29.
  9. A. G. Naoum and F. H. Al-Alwan, Dedekind modules, Comm. Algebra 24 (1996), 397-412. https://doi.org/10.1080/00927879608825576
  10. B. Sarac, P. F. Smith, and Y. Tiras, On Dedekind modules, Comm. Algebra 35 (2007), 1533-1538. https://doi.org/10.1080/00927870601169051
  11. P. F. Smith, Some remarks on multiplication modules, Arch. Math. 50 (1988), 223-235. https://doi.org/10.1007/BF01187738
  12. U. Tekir, A note on Dedekind and ZPI modules, Algebra Colloq. 13 (2006), 41-45. https://doi.org/10.1142/S1005386706000071