CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Strongly $0$-dimensional Modules

  Published:2013-03-08
 Printed: Mar 2014
  • Kürşat Hakan Oral,
    Yildiz Technical University, Department of Mathematics, Davutpasa Campus, Esenler, 34210, Istanbul, Turkey
  • Neslihan Ayşen Özkirişci,
    Yildiz Technical University, Department of Mathematics, Davutpasa Campus, Esenler, 34210, Istanbul, Turkey
  • Ünsal Tekir,
    Marmara University, Department of Mathematics, 34722, Ziverbey, Kadıköy, Istanbul, Turkey
Format:   LaTeX   MathJax   PDF  

Abstract

In a multiplication module, prime submodules have the property, if a prime submodule contains a finite intersection of submodules then one of the submodules is contained in the prime submodule. In this paper, we generalize this property to infinite intersection of submodules and call such prime submodules strongly prime submodule. A multiplication module in which every prime submodule is strongly prime will be called strongly 0-dimensional module. It is also an extension of strongly 0-dimensional rings. After this we investigate properties of strongly 0-dimensional modules and give relations of von Neumann regular modules, Q-modules and strongly 0-dimensional modules.
Keywords: strongly 0-dimensional rings, Q-module, Von Neumann regular module strongly 0-dimensional rings, Q-module, Von Neumann regular module
MSC Classifications: 13C99, 16D10 show english descriptions None of the above, but in this section
General module theory
13C99 - None of the above, but in this section
16D10 - General module theory
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/