Iséki spaces of semirings
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914916952178688 |
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| author | Goswami, Amartya |
| author_facet | Goswami, Amartya |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14769 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Iséki spaces of semirings Goswami, Amartya Rings and Algebras 16Y60 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 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. |
| title | Iséki spaces of semirings |
| topic | Rings and Algebras 16Y60 |
| url | https://arxiv.org/abs/2212.14769 |