Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

TOPOLOGICAL DIMENSION OF PSEUDO-PRIME SPECTRUM OF MODULES

  • Received : 2016.11.04
  • Accepted : 2017.06.05
  • Published : 2017.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

Different topological dimensions related to the pseudo-prime spectrum of topological modules are studied. An example of topological modules is introduced. Also, we give a result about Noetherianness of the pseudo-prime spectrum of topological modules.

Keywords

References

  1. A. Barnard, Multiplication modules, J. Algebra 71 (1981), no. 1, 174-178. https://doi.org/10.1016/0021-8693(81)90112-5
  2. N. Bourbaki, Elements of Mathematics. Commutative Algebra, Addison-Wesley, Publishing Co., 1972.
  3. M. P. Brodmann and R. Y. Sharp, Local Cohomology an Algebraic Introduction with Geometric Applications, Cambridge Univercity Press, 1998.
  4. Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra 16 (1988), no. 4, 755-779. https://doi.org/10.1080/00927878808823601
  5. D. Hassanzadeh-Lelekaami and H. Roshan-Shekalgourabi, Pseudo-prime submodules of modules, Math. Rep. (Bucur.) 18(68) (2016), no. 4, 591-608.
  6. I. Kaplansky, Commutative rings, University of Chicago Press, 1974.
  7. C.-P. Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math. 33 (2007), no. 1, 125-143.
  8. H.Matsumura, Commutative ring theory, Cambridge: Campridge University, Press, 1986.
  9. J. Ohm and R. L. Pendleton, Rings with Noetherian spectrum, Duke Math. J. 35 (1968), 631-640. https://doi.org/10.1215/S0012-7094-68-03565-5