Second Spectrum of Modules and Spectral Spaces

Ceken S., Alkan M.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, cilt.42, sa.1, ss.153-169, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s40840-017-0473-0
  • Dergi Adı: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.153-169
  • Anahtar Kelimeler: Second submodule, Cotop module, Dual Zariski topology, Spectral space, ZARISKI TOPOLOGY, PRIME SPECTRUM, DUAL NOTION, RINGS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.