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Second Spectrum of Modules and Spectral Spaces

  • Seçil ÇekenEmail author
  • Mustafa Alkan
Article

Abstract

Let R be a commutative ring with identity and \(\hbox {Spec}^{s}(M)\) denote the set all second submodules of an R-module M. In this paper, we investigate various properties of \(\hbox {Spec}^{s}(M)\) with respect to different topologies. We investigate the dual Zariski topology from the point of view of separation axioms, spectral spaces and combinatorial dimension. We establish conditions for \(\hbox {Spec}^{s}(M)\) to be a spectral space with respect to quasi-Zariski topology and second classical Zariski topology. We also present some conditions under which a module is cotop.

Keywords

Second submodule Cotop module Dual Zariski topology Spectral space 

Mathematics Subject Classification

13C13 13C05 13C99 

Notes

Acknowledgements

The authors would like to thank the Scientific Technological Research Council of Turkey (TUBITAK) for funding this work through the project 114F381. The M. Alkan is supported by the Scientific Research Project Administration of Akdeniz University.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Department of Mathematics-Computerİstanbul Aydın UniversityIstanbulTurkey
  2. 2.Department of MathematicsAkdeniz UniversityAntalyaTurkey

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