Fuzzy Spectral Spaces and Fuzzy Congruences of a Heyting ADL
In this paper, the space Fp of fuzzy prime ideals of Heyting almost distributive lattice H is studied, and it is shown that the collection of all sets Mη is a topology on Fp, where η is a fuzzy ideal on H and Mη=θ∈Fp|η⊈θ. The only compact subset of the space Fp is given. A fuzzy congruence relation...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/4926900 |
| _version_ | 1797945536495484928 |
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| author | Yeshiwas Mebrat Gubena Teferi Getachew Alemayehu |
| author_facet | Yeshiwas Mebrat Gubena Teferi Getachew Alemayehu |
| author_sort | Yeshiwas Mebrat Gubena |
| collection | DOAJ |
| description | In this paper, the space Fp of fuzzy prime ideals of Heyting almost distributive lattice H is studied, and it is shown that the collection of all sets Mη is a topology on Fp, where η is a fuzzy ideal on H and Mη=θ∈Fp|η⊈θ. The only compact subset of the space Fp is given. A fuzzy congruence relation Θ on H is defined, and the homomorphism between the set of all fuzzy ideals of H and the set of all fuzzy ideals of H/Θ is established. Furthermore, we established an isomorphism between fuzzy spectrum of H and fuzzy spectrum of H/Θ. |
| first_indexed | 2024-04-10T20:57:43Z |
| format | Article |
| id | doaj.art-603b6ec12cab4eb18ad2ffcf980f5378 |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-04-10T20:57:43Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-603b6ec12cab4eb18ad2ffcf980f53782023-01-23T00:56:09ZengHindawi LimitedJournal of Mathematics2314-47852023-01-01202310.1155/2023/4926900Fuzzy Spectral Spaces and Fuzzy Congruences of a Heyting ADLYeshiwas Mebrat Gubena0Teferi Getachew Alemayehu1Department of MathematicsDepartment of MathematicsIn this paper, the space Fp of fuzzy prime ideals of Heyting almost distributive lattice H is studied, and it is shown that the collection of all sets Mη is a topology on Fp, where η is a fuzzy ideal on H and Mη=θ∈Fp|η⊈θ. The only compact subset of the space Fp is given. A fuzzy congruence relation Θ on H is defined, and the homomorphism between the set of all fuzzy ideals of H and the set of all fuzzy ideals of H/Θ is established. Furthermore, we established an isomorphism between fuzzy spectrum of H and fuzzy spectrum of H/Θ.http://dx.doi.org/10.1155/2023/4926900 |
| spellingShingle | Yeshiwas Mebrat Gubena Teferi Getachew Alemayehu Fuzzy Spectral Spaces and Fuzzy Congruences of a Heyting ADL Journal of Mathematics |
| title | Fuzzy Spectral Spaces and Fuzzy Congruences of a Heyting ADL |
| title_full | Fuzzy Spectral Spaces and Fuzzy Congruences of a Heyting ADL |
| title_fullStr | Fuzzy Spectral Spaces and Fuzzy Congruences of a Heyting ADL |
| title_full_unstemmed | Fuzzy Spectral Spaces and Fuzzy Congruences of a Heyting ADL |
| title_short | Fuzzy Spectral Spaces and Fuzzy Congruences of a Heyting ADL |
| title_sort | fuzzy spectral spaces and fuzzy congruences of a heyting adl |
| url | http://dx.doi.org/10.1155/2023/4926900 |
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