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Strongly 0-dimensional Modules

Published online by Cambridge University Press:  20 November 2018

Kürşat Hakan Oral ,
Neslihan Ayşen Özkirişci  and
Ünsal Tekir
Kürşat Hakan Oral
Affiliation:
Yildiz TechnicalUniversity, Department ofMathematics, Davutpasa Campus, Esenler, 34210, Istanbul, Turkey e-mail: [email protected]@yildiz.edu.tr
Neslihan Ayşen Özkirişci
Affiliation:
Marmara University, Department of Mathematics, 34722, Ziverbey, Kadıköy, Istanbul, Turkey e-mail: [email protected]
Ünsal Tekir
Affiliation:
Yildiz TechnicalUniversity, Department ofMathematics, Davutpasa Campus, Esenler, 34210, Istanbul, Turkey e-mail: [email protected]@yildiz.edu.tr
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Abstract

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In a multiplication module, prime submodules have the following 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 submodules. A multiplication module in which every prime submodule is strongly prime will be called a 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

13C9916D10Strongly 0-dimensional ringsQ-moduleVon Neumann regular module
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 1 , 14 March 2014 , pp. 159 - 165
Copyright
Copyright © Canadian Mathematical Society 2014

References

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