On the Weakly Second Spectrum of a Module

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Ceken S., ALKAN M.

FILOMAT, vol.30, no.4, pp.1013-1020, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1604013c
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1013-1020
  • Keywords: Weakly second submodule, second submodule, weakly second radical, weakly second classical Zariski topology, DUAL NOTION, ZARISKI TOPOLOGY, PRIME
  • Akdeniz University Affiliated: Yes


In this paper, we extend the definition of weakly second submodule of a module over a commutative ring to a module over an arbitrary ring. First, we investigate some properties of weakly second submodules. We define the notion of weakly second radical of a submodule and determine the weakly second radical of some modules. We also define the notion of weak m*-system and characterize the weakly second radical of a submodule in terms of weak m*-systems. Then we introduce and study a topology on the set of all weakly second submodules of a module. We give some results concerning irreducible subsets, irreducible components and compactness of this topological space. Finally, we investigate this topological space from the point of view of spectral spaces.