A sheaf on the second spectrum of a module

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Çeken S., ALKAN M.

Communications in Algebra, vol.46, no.12, pp.5487-5499, 2018 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 46 Issue: 12
  • Publication Date: 2018
  • Doi Number: 10.1080/00927872.2018.1472270
  • Journal Name: Communications in Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5487-5499
  • Keywords: dual Zariski topology, Second submodule, sheaf of modules
  • Open Archive Collection: AVESIS Open Access Collection
  • Trakya University Affiliated: Yes

Abstract

Let R be a commutative ring with identity and Spec s (M) denote the set all second submodules of an R-module M. In this paper, we construct and study a sheaf of modules, denoted by O(N,M), on Spec s (M) equipped with the dual Zariski topology of M, where N is an R-module. We give a characterization of the sections of the sheaf O(N,M) in terms of the ideal transform module. We present some interrelations between algebraic properties of N and the sections of O(N,M). We obtain some morphisms of sheaves induced by ring and module homomorphisms.