On $z$-ideals and $z$-closure operations of semirings, I
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909595145863168 |
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| author | Goswami, Amartya |
| author_facet | Goswami, Amartya |
| contents | The aim of this series of papers is to study $z$-ideals of semirings. In this article, we introduce some distinguished classes of $z$-ideals of semirings, which include $z$-prime, $z$-semiprime, $z$-irreducible, and $z$-strongly irreducible ideals and study some of their properties. Using a $z$-closure operator, we show the equivalence of these classes of ideals with the corresponding $z$-ideals that are prime, semirprime, irreducible, and strongly irreducible, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09052 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $z$-ideals and $z$-closure operations of semirings, I Goswami, Amartya Rings and Algebras 16Y60, 16D25 The aim of this series of papers is to study $z$-ideals of semirings. In this article, we introduce some distinguished classes of $z$-ideals of semirings, which include $z$-prime, $z$-semiprime, $z$-irreducible, and $z$-strongly irreducible ideals and study some of their properties. Using a $z$-closure operator, we show the equivalence of these classes of ideals with the corresponding $z$-ideals that are prime, semirprime, irreducible, and strongly irreducible, respectively. |
| title | On $z$-ideals and $z$-closure operations of semirings, I |
| topic | Rings and Algebras 16Y60, 16D25 |
| url | https://arxiv.org/abs/2410.09052 |