Relationship Between Hyper MV -algebras and Hyperlattices
Sh. Ghorbani, et al. [9], generalized the concept of MV -algebras and defined the notion of hyper MV -algebras. Now, in this paper, we try to prove that any hyper MV -algebra is a hyperlattice. First we prove that any hyper MV -algebra that satisfies the semi negation property is a hyperlattice. The...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2016-12-01
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| Series: | Annals of the West University of Timisoara: Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/awutm-2016-0016 |
| _version_ | 1818469172528545792 |
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| author | Borzooei R. A. Radfar Akefe Niazian Sogol |
| author_facet | Borzooei R. A. Radfar Akefe Niazian Sogol |
| author_sort | Borzooei R. A. |
| collection | DOAJ |
| description | Sh. Ghorbani, et al. [9], generalized the concept of MV -algebras and defined the notion of hyper MV -algebras. Now, in this paper, we try to prove that any hyper MV -algebra is a hyperlattice. First we prove that any hyper MV -algebra that satisfies the semi negation property is a hyperlattice. Then with a computer program, we show that any hyper MV -algebra of order less than 6, is a hyperlattice. Finally, we claim that this result is correct for any hyper MV -algebra. |
| first_indexed | 2024-04-13T21:21:07Z |
| format | Article |
| id | doaj.art-899372bcb5fc49a99b44200e68833085 |
| institution | Directory Open Access Journal |
| issn | 1841-3307 |
| language | English |
| last_indexed | 2024-04-13T21:21:07Z |
| publishDate | 2016-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annals of the West University of Timisoara: Mathematics and Computer Science |
| spelling | doaj.art-899372bcb5fc49a99b44200e688330852022-12-22T02:29:29ZengSciendoAnnals of the West University of Timisoara: Mathematics and Computer Science1841-33072016-12-01542759410.1515/awutm-2016-0016awutm-2016-0016Relationship Between Hyper MV -algebras and HyperlatticesBorzooei R. A.0Radfar Akefe1Niazian Sogol2Department of Mathematics, Shahid Beheshti University Tehran, Iran (Islamic Republic of)Department of Mathematics, Payame Noor University p.o.box 19395-3697 Tehran, Iran (Islamic Republic of)Tehran Medical Sciences Branch, Islamic Azad University Tehran, Iran (Islamic Republic of)Sh. Ghorbani, et al. [9], generalized the concept of MV -algebras and defined the notion of hyper MV -algebras. Now, in this paper, we try to prove that any hyper MV -algebra is a hyperlattice. First we prove that any hyper MV -algebra that satisfies the semi negation property is a hyperlattice. Then with a computer program, we show that any hyper MV -algebra of order less than 6, is a hyperlattice. Finally, we claim that this result is correct for any hyper MV -algebra.https://doi.org/10.1515/awutm-2016-0016mv -algebrahyper mv -algebrahyperlattice |
| spellingShingle | Borzooei R. A. Radfar Akefe Niazian Sogol Relationship Between Hyper MV -algebras and Hyperlattices Annals of the West University of Timisoara: Mathematics and Computer Science mv -algebra hyper mv -algebra hyperlattice |
| title | Relationship Between Hyper MV -algebras and Hyperlattices |
| title_full | Relationship Between Hyper MV -algebras and Hyperlattices |
| title_fullStr | Relationship Between Hyper MV -algebras and Hyperlattices |
| title_full_unstemmed | Relationship Between Hyper MV -algebras and Hyperlattices |
| title_short | Relationship Between Hyper MV -algebras and Hyperlattices |
| title_sort | relationship between hyper mv algebras and hyperlattices |
| topic | mv -algebra hyper mv -algebra hyperlattice |
| url | https://doi.org/10.1515/awutm-2016-0016 |
| work_keys_str_mv | AT borzooeira relationshipbetweenhypermvalgebrasandhyperlattices AT radfarakefe relationshipbetweenhypermvalgebrasandhyperlattices AT niaziansogol relationshipbetweenhypermvalgebrasandhyperlattices |