t-Prüfer Modules

  • Kim, Myeong Og ;
  • Kim, Hwankoo ;
  • Oh, Dong Yeol
  • Received : 2012.12.08
  • Accepted : 2013.04.19
  • Published : 2013.09.23


In this article, we characterize t-Pr$\ddot{u}$fer modules in the class of faithful multiplication modules. As a corollary, we also characterize Krull modules. Several properties of a $t$-invertible submodule of a faithful multiplication module are given.


t-Prufer module;faithful multiplication module;Krull module;t-invertible submodule


  1. F. H. Al-Alwan and A. G. Naoum, Dedekind modules, Comm. Algebra, 24(1996), 397-421.
  2. F. H. Al-Alwan and A. G. Naoum, Dense submodules of multiplication modules, Comm. Algebra, 24(1996), 413-424.
  3. M. Ali, Invertiblity of multiplication modules, New Zealand J. Math., 35(2006), 17-29.
  4. M. Ali, Some remarks on generalized GCD domains, Comm. Algebra, 36(2008), 142-164.
  5. M. Ali, Invertiblity of multiplication modules II, New Zealand J. Math., 39(2009), 45-64.
  6. M. Ali and D. J. Smith, Some remarks on multiplication and projective modules, Comm. Algebra, 32(2004), 3897-3909.
  7. M. Alkan, B Sarac, and Y. Tiras, Dedekind modules, Comm. Algebra, 33(2005), 1617-1626.
  8. M. Alkan and Y. Tiras, Prime modules and submodules, Comm. Algebra, 31(2003), 5253-5261.
  9. M. Alkan and Y. Tiras, On Invertible and dense submodules, Comm. Algebra, 32(2004), 3911-3919.
  10. Y. Al-Shaniafi and D. D Anderson, Multiplication modules and the ideal ${\theta}(M)$, Comm. Algebra, 30(2002), 3383-3390.
  11. D. D. Anderson, On t-invertibility IV, Factorization in integral domains (Iowa City, IA, 1996), 221-225, Lecture Notes in Pure and Appl. Math., 189, Dekker, New York, 1997.
  12. Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(1988), 755-739.
  13. V. Erdogdu, Multiplication modules which are distributive, J. Pure Appl. Algebra, 54(1988), 209-213.
  14. E. Houston and M. Zafrullah, Integral domains in which each t-ideal is divisorial, Mich. Math. J. 35(1988), 291-300.
  15. B. G. Kang, On the converse of a well-known fact about Krull domains, J. Algebra, 124(1989), 284-299.
  16. H. Kim and M. O. Kim , Krull modules, Algebra Colloq., 20(2013), 464-474.
  17. S. Malik, J. L. Mott, and M. Zafrullah, On t-invertibility, Comm. Algebra, 16(1988), 149-170.
  18. J. L. Mott and M. Zafrullah, On Krull domains, Arch. Math., 56(1991), 559-568.
  19. P. F. Smith, Some remarks on multiplication modules, Arch. Math., 50(1988), 223-235.
  20. M. Zafrullah, Ascending chain condition and star operations, Comm. Algebra, 17(1989), 1523-1533.


Supported by : National Research Foundation of Korea(NRF)