Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

FINITELY GENERATED gr-MULTIPLICATION MODULES

  • Published : 2012.11.15
⟨ Previous Next ⟩

Abstract

In this paper, we investigate when gr-multiplication modules are finitely generated and show that if M is a finitely generated gr-multiplication R-module then there is a lattice isomorphism between the lattice of all graded ideals I of R containing ann(M) and the lattice of all graded submodules of M.

Keywords

References

  1. S. E. Atani and R. E. Atani, Graded multiplication modules and the graded ideal ${\theta}_g(M)$, Turkish J. Math. 35 (2011), no. 1, 1-9.
  2. A. Barnard, Multiplication modules, J. Algebra. 71 (1981), no. 1, 174-178. https://doi.org/10.1016/0021-8693(81)90112-5
  3. Z. A. El-Bast and P.F. Smith, Multiplication modules, Comm. Algebra. 16 (1988), no. 4, 755-779. https://doi.org/10.1080/00927878808823601
  4. J. Escoriza and B. Torrecillas, Multiplication objects in commutative Grothendieck categories, Comm. Algebra. 26 (1998), no. 6, 1867-1883. https://doi.org/10.1080/00927879808826244
  5. R. Gilmer, An existence theorem for non-Noetherian rings, Amer. Math. Monthly. 77 (1970), 621-623. https://doi.org/10.2307/2316741
  6. A. G. Naoum, B. A. Al-Hashimi, and H. R. Hassan, Maximal, prime and primary submodules of finitely generated multiplication modules, Dirasat Ser. B Pure Appl. Sci. 18 (1991), no. 1, 7-17.
  7. K. Nekooei, On finitely generated multiplication modules, Czechoslovak Math. J. 55(130) (2005), no. 2, 503-510.
  8. N. Zamani, Finitely generated graded multiplication modules, Glasg. Math. J. 53 (2011), no. 3, 693-705. https://doi.org/10.1017/S0017089511000279