Reflectional topology in MV-algebras
In this paper, we define soaker ideals in an MV-algebra, and study the relationships between soaker ideals and the other ideals in an involutive MV -algebras. Then we introduce a topology on the set of all the soaker ideals, which we call reflectional topology, and give a basis for it. By defining t...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2022-01-01
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| Series: | Categories and General Algebraic Structures with Applications |
| Subjects: | |
| Online Access: | https://cgasa.sbu.ac.ir/article_101907_2ded973e84d70c127553282fbd184a99.pdf |
| _version_ | 1818688885455060992 |
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| author | Fereshteh Forouzesh Naser Hosseini |
| author_facet | Fereshteh Forouzesh Naser Hosseini |
| author_sort | Fereshteh Forouzesh |
| collection | DOAJ |
| description | In this paper, we define soaker ideals in an MV-algebra, and study the relationships between soaker ideals and the other ideals in an involutive MV -algebras. Then we introduce a topology on the set of all the soaker ideals, which we call reflectional topology, and give a basis for it. By defining the notion of join-soaker ideals, we show that the reflectional topology is compact. We also give a characterization of connectedness of the reflectional topology. Finally, we investigate the properties of T0 and T1-space in this topology. |
| first_indexed | 2024-12-17T12:01:19Z |
| format | Article |
| id | doaj.art-d9f4894f159947d79c8c9cb73aac1d76 |
| institution | Directory Open Access Journal |
| issn | 2345-5853 2345-5861 |
| language | English |
| last_indexed | 2024-12-17T12:01:19Z |
| publishDate | 2022-01-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj.art-d9f4894f159947d79c8c9cb73aac1d762022-12-21T21:49:50ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612022-01-0116110.52547/cgasa.2021.101907101907Reflectional topology in MV-algebrasFereshteh Forouzesh0Naser Hosseini1Faculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran.Department of Pure Mathematics, Faculty of Math and Computers, Shahid Bahonar University of Kerman, Kerman, IranIn this paper, we define soaker ideals in an MV-algebra, and study the relationships between soaker ideals and the other ideals in an involutive MV -algebras. Then we introduce a topology on the set of all the soaker ideals, which we call reflectional topology, and give a basis for it. By defining the notion of join-soaker ideals, we show that the reflectional topology is compact. We also give a characterization of connectedness of the reflectional topology. Finally, we investigate the properties of T0 and T1-space in this topology.https://cgasa.sbu.ac.ir/article_101907_2ded973e84d70c127553282fbd184a99.pdffinitely meet-irreducibleinvolutive(soakerjoin-soaker) idealreflectional topology |
| spellingShingle | Fereshteh Forouzesh Naser Hosseini Reflectional topology in MV-algebras Categories and General Algebraic Structures with Applications finitely meet-irreducible involutive (soaker join-soaker) ideal reflectional topology |
| title | Reflectional topology in MV-algebras |
| title_full | Reflectional topology in MV-algebras |
| title_fullStr | Reflectional topology in MV-algebras |
| title_full_unstemmed | Reflectional topology in MV-algebras |
| title_short | Reflectional topology in MV-algebras |
| title_sort | reflectional topology in mv algebras |
| topic | finitely meet-irreducible involutive (soaker join-soaker) ideal reflectional topology |
| url | https://cgasa.sbu.ac.ir/article_101907_2ded973e84d70c127553282fbd184a99.pdf |
| work_keys_str_mv | AT fereshtehforouzesh reflectionaltopologyinmvalgebras AT naserhosseini reflectionaltopologyinmvalgebras |