Second Spectrum of Modules and Spectral Spaces


Ceken S., Alkan M.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.42, no.1, pp.153-169, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1007/s40840-017-0473-0
  • Journal Name: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.153-169
  • Keywords: Second submodule, Cotop module, Dual Zariski topology, Spectral space, ZARISKI TOPOLOGY, PRIME SPECTRUM, DUAL NOTION, RINGS
  • Akdeniz University Affiliated: Yes

Abstract

Let R be a commutative ring with identity and Specs(M) denote the set all second submodules of an R-module M. In this paper, we investigate various properties of Specs(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 Specs(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.