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...
| Main Authors: | , , |
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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 |
| Summary: | 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. |
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| ISSN: | 2345-5853 2345-5861 |