Is\'eki spaces of semirings
Abstract
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\'eki space is quasi-compact whenever the semiring is Noetherian. We characterize Is\'eki 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\'eki spaces and show that the strongly connectedness of an Is\'eki space implies the existence of non-trivial idempotent elements of semirings.
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