Iséki spaces of semirings

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The aim of this paper is to study Iséki spaces of distinguished classes of ideals of a semiring endowed with a topology. We show that every Iséki space is quasi-compact whenever the semiring is Noetherian. We characterize Iséki spaces for which every non-empty irreducible closed subset has a unique generic point. Furthermore, we provide a sufficient condition for the connectedness of Iséki spaces and show that the strongly connectedness of an Iséki space implies the existence of non-trivial idempotent elements of semirings.

Original languageEnglish
Pages (from-to)677-686
Number of pages10
JournalBolletino dell Unione Matematica Italiana
Issue number4
Publication statusPublished - Dec 2023


  • Coarse lower topology
  • Radical
  • Semiring
  • Sober space
  • Spectral space
  • Strongly irreducible ideal

ASJC Scopus subject areas

  • General Mathematics


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