http://dx.doi.org/10.4153/CMB-2013-004-3
7 pages
Published:2013-03-08
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
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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.
© Canadian Mathematical Society, 2013
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