On the Zariski topology over an L-module M

ÇALLIALP F., Ulucak G., TEKİR Ü.

TURKISH JOURNAL OF MATHEMATICS, vol.41, no.2, pp.326-336, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.3906/mat-1502-31
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.326-336
  • Keywords: Lattice, lattice module, prime element, Zariski topology, PRIME SPECTRUM
  • Marmara University Affiliated: Yes

Abstract

Let L be a multiplicative lattice and M be an L-module. In this study, we present a topology said to be the Zariski topology over sigma(M), the collection of all prime elements of an L-module M. We research some results on the Zariski topology over sigma(M). We show that the topology is a T-0-space and a T-1-space under some conditions. Some properties and results are studied for the topology over sigma-(L), the collection of all prime elements of a multiplicative lattice L.