Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SECOND CLASSICAL ZARISKI TOPOLOGY ON SECOND SPECTRUM OF LATTICE MODULES

  • Received : 2019.12.25
  • Accepted : 2020.07.21
  • Published : 2020.09.30
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Abstract

Let M be a lattice module over a C-lattice L. Let Specs(M) be the collection of all second elements of M. In this paper, we consider a topology on Specs(M), called the second classical Zariski topology as a generalization of concepts in modules and investigate the interplay between the algebraic properties of a lattice module M and the topological properties of Specs(M). We investigate this topological space from the point of view of spectral spaces. We show that Specs(M) is always T0-space and each finite irreducible closed subset of Specs(M) has a generic point.

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References

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