The prime state ideal theorem in state residuated lattices
The aim of this paper is to establish the prime state ideal theorem in state residuated lattices (SRLs). We study the state ideals lattice $\mathcal{SI}(L)$ of astate residuated lattice $(L, \varphi)$ andprove that it is a complete Brouwerian lattice inwhich the meet and the join of any two compact...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2023-02-01
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| Series: | Categories and General Algebraic Structures with Applications |
| Subjects: | |
| Online Access: | https://cgasa.sbu.ac.ir/article_103288_7c80a9cedf8e1ba5002830b5d68d31cf.pdf |
| _version_ | 1797870019979247616 |
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| author | Francis Woumfo Etienne Romuald Temgoua Celestin Lele |
| author_facet | Francis Woumfo Etienne Romuald Temgoua Celestin Lele |
| author_sort | Francis Woumfo |
| collection | DOAJ |
| description | The aim of this paper is to establish the prime state ideal theorem in state residuated lattices (SRLs). We study the state ideals lattice $\mathcal{SI}(L)$ of astate residuated lattice $(L, \varphi)$ andprove that it is a complete Brouwerian lattice inwhich the meet and the join of any two compact elements are compact (coherent frame). We characterize the notion of prime state ideals in SRLs. In addition, we establish the condition for which thelattice $\mathcal{SI}(L)$ is a Boolean algebra. |
| first_indexed | 2024-04-10T00:21:47Z |
| format | Article |
| id | doaj.art-214505cfa77a41d287a4e922f8f14a17 |
| institution | Directory Open Access Journal |
| issn | 2345-5853 2345-5861 |
| language | English |
| last_indexed | 2024-04-10T00:21:47Z |
| publishDate | 2023-02-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj.art-214505cfa77a41d287a4e922f8f14a172023-03-15T21:26:12ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612023-02-0118113115310.52547/cgasa.2023.103288103288The prime state ideal theorem in state residuated latticesFrancis Woumfo0Etienne Romuald Temgoua1Celestin Lele2Departement of Mathematics and Computer Science, Faculty of Sciences, University of Dschang, Dschang, CameroonDepartment of Mathematics, école Normale Supérieure de Yaoundé, University of Yaoundé 1, Yaoundé, CameroonDepartment of Mathematics and Computer Science, Faculty of Science, University of Dschang, Dschang, CameroonThe aim of this paper is to establish the prime state ideal theorem in state residuated lattices (SRLs). We study the state ideals lattice $\mathcal{SI}(L)$ of astate residuated lattice $(L, \varphi)$ andprove that it is a complete Brouwerian lattice inwhich the meet and the join of any two compact elements are compact (coherent frame). We characterize the notion of prime state ideals in SRLs. In addition, we establish the condition for which thelattice $\mathcal{SI}(L)$ is a Boolean algebra.https://cgasa.sbu.ac.ir/article_103288_7c80a9cedf8e1ba5002830b5d68d31cf.pdfstate idealframeresiduated lattice |
| spellingShingle | Francis Woumfo Etienne Romuald Temgoua Celestin Lele The prime state ideal theorem in state residuated lattices Categories and General Algebraic Structures with Applications state ideal frame residuated lattice |
| title | The prime state ideal theorem in state residuated lattices |
| title_full | The prime state ideal theorem in state residuated lattices |
| title_fullStr | The prime state ideal theorem in state residuated lattices |
| title_full_unstemmed | The prime state ideal theorem in state residuated lattices |
| title_short | The prime state ideal theorem in state residuated lattices |
| title_sort | prime state ideal theorem in state residuated lattices |
| topic | state ideal frame residuated lattice |
| url | https://cgasa.sbu.ac.ir/article_103288_7c80a9cedf8e1ba5002830b5d68d31cf.pdf |
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