On $z$-elements of multiplicative lattices
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908338608930816 |
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| author | Dube, Themba Goswami, Amartya |
| author_facet | Dube, Themba Goswami, Amartya |
| contents | The aim of this paper is to investigate further properties of $z$-elements in multiplicative lattices. We utilize $z$-closure operators to extend several properties of $z$-ideals to $z$-elements and introduce various distinguished subclasses of $z$-elements, such as $z$-prime, $z$-semiprime, $z$-primary, $z$-irreducible, and $z$-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where $z$-elements are closed under finite products and a representation of $z$-elements in terms of $z$-irreducible elements in $z$-Noetherian multiplicative lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $z$-elements of multiplicative lattices Dube, Themba Goswami, Amartya Rings and Algebras 06F07, 06F99, 06B23 The aim of this paper is to investigate further properties of $z$-elements in multiplicative lattices. We utilize $z$-closure operators to extend several properties of $z$-ideals to $z$-elements and introduce various distinguished subclasses of $z$-elements, such as $z$-prime, $z$-semiprime, $z$-primary, $z$-irreducible, and $z$-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where $z$-elements are closed under finite products and a representation of $z$-elements in terms of $z$-irreducible elements in $z$-Noetherian multiplicative lattices. |
| title | On $z$-elements of multiplicative lattices |
| topic | Rings and Algebras 06F07, 06F99, 06B23 |
| url | https://arxiv.org/abs/2405.11670 |