Is\'{e}ki spaces of semirings

The aim of this paper is to study Iseki spaces of distinguished classes of ideals of a semiring endowed with a topology. We show that every Is\'{e}ki space is quasi-compact whenever the semiring is Noetherian. We characterize Is\'{e}ki spaces for which every non-empty irreducible closed su...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Author: Goswami, Amartya
Format: Article
Language:English
Subjects:
Rings (mathematics)
Topology
Online Access:Get full text
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Summary:The aim of this paper is to study Iseki spaces of distinguished classes of ideals of a semiring endowed with a topology. We show that every Is\'{e}ki space is quasi-compact whenever the semiring is Noetherian. We characterize Is\'{e}ki spaces for which every non-empty irreducible closed subset has a unique generic point. Furthermore, we provide a sufficient condition for the connectedness of Is\'{e}ki spaces and show that the strongly connectedness of an Is\'{e}ki space implies the existence of non-trivial idempotent elements of semirings.
ISSN:2331-8422