Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

STRONGLY IRREDUCIBLE SUBMODULES

  • Published : 2005.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper is motivated by the results in [6]. We study some properties of strongly irreducible submodules of a module. In fact, our objective is to investigate strongly irreducible modules and to examine in particular when sub modules of a module are strongly irreducible. For example, we show that prime submodules of a multiplication module are strongly irreducible, and a characterization is given of a multiplication module over a Noetherian ring which contain a non-prime strongly irreducible submodule.

Keywords

References

  1. D. D. Anderson and Y. Al-Shaniafi, Multiplication Modules and The Ideal ${\theta}$(M), Comm. Algebra 30 (2002), 3383-3390 https://doi.org/10.1081/AGB-120004493
  2. A. Barnard, Multiplication Modules, J. Algebra 71 (1981), 174-178 https://doi.org/10.1016/0021-8693(81)90112-5
  3. S. Ebrahimi Atani, On Secondary Modules Over Pullback Rings, Comm. Algebra 30 (2002), 2675-2685 https://doi.org/10.1081/AGB-120003982
  4. S. Ebrahimi Atani, Submodules of Secondary Modules, Int. J. Math. Math. Sci. 31 (2002), 321-327 https://doi.org/10.1155/S0161171202107149
  5. Z. A. Elbast and P. F. Smith, Multiplication Modules, Comm. Algebra 16 (1988), 755-779 https://doi.org/10.1080/00927878808823601
  6. W. J. Heinzer and L. J. Ratlif and D. E. Rush, Strongly Irreducible Ideals of a Commutative Ring, J. Pure Appl. Algebra 166 (2002), 267-275 https://doi.org/10.1016/S0022-4049(01)00043-3
  7. C. Jensen, Arithmetical Rings, Acta Math. Sci. Hungar, 17 (1966), 115-123 https://doi.org/10.1007/BF02020446
  8. I. Kaplansky, Commutative Rings, University of Chicago Press, Chicago, 1974
  9. D. G. Northcott, Lessons On Rings, Modules and Multiplicities, Cambridge University Press, London, 1968
  10. Y. S. Park and C. W. Choi, Multiplication Modules and Characteristic Submodules, Bull. Korean Math. Soc. 32 (1995), 321-327
  11. S. Singh and Y. Al-shaniafi, Multiplication Modules, Comm. Algebra 29 (2001), 2597-2609 https://doi.org/10.1081/AGB-100002410
  12. P. F. Smith, Some Remarks On Multiplication Modules, Arch. Math. 50 (1988), 223-235 https://doi.org/10.1007/BF01187738
  13. Y. Tiras, A. Tercan and A. Harmanci, Prime Submodules, Honam Math. J. 18 (1996), 5-15

Cited by

  1. Zariski Topologies for Coprime and Second Submodules vol.22, pp.01, 2015, https://doi.org/10.1142/S1005386715000061
  2. ON THE NOTION OF STRONG IRREDUCIBILITY AND ITS DUAL vol.12, pp.06, 2013, https://doi.org/10.1142/S0219498813500126