On residuated n-lattice
In this paper, we introduce residuated n-lattice: a variety of residuated semigroup equipped with binary hyperoperations n-sup and n-inf. We define the left bound, right bound, n-supremum, n-infimum, maximum and minimum with respect to it′s relation. By these way, the notion of residuated semigroup...
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| Format: | Article |
| Language: | English |
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Sciendo
2025-03-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
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| Online Access: | https://doi.org/10.2478/auom-2025-0014 |
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| author | Zahiri Saeide Saeid Arsham Borumand |
| author_facet | Zahiri Saeide Saeid Arsham Borumand |
| author_sort | Zahiri Saeide |
| collection | DOAJ |
| description | In this paper, we introduce residuated n-lattice: a variety of residuated semigroup equipped with binary hyperoperations n-sup and n-inf. We define the left bound, right bound, n-supremum, n-infimum, maximum and minimum with respect to it′s relation. By these way, the notion of residuated semigroup has been generalized. Some examples of residuated n-lattice have been gave, then we show that our definition is an extention of the old ones. Also, we state and prove some theorems in this structure. |
| format | Article |
| id | doaj-art-7fb4b162b48449bd8a646894702ea097 |
| institution | OA Journals |
| issn | 1844-0835 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj-art-7fb4b162b48449bd8a646894702ea0972025-08-20T02:08:14ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352025-03-0133128129110.2478/auom-2025-0014On residuated n-latticeZahiri Saeide0Saeid Arsham Borumand11Department of Mathematics, Faculty of Science, Higher Education Center of Eghlid, Eghlid, Iran.2Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran; Adjunct Professor, Saveetha School of Engineering, SIMATS, Chennai, India.In this paper, we introduce residuated n-lattice: a variety of residuated semigroup equipped with binary hyperoperations n-sup and n-inf. We define the left bound, right bound, n-supremum, n-infimum, maximum and minimum with respect to it′s relation. By these way, the notion of residuated semigroup has been generalized. Some examples of residuated n-lattice have been gave, then we show that our definition is an extention of the old ones. Also, we state and prove some theorems in this structure.https://doi.org/10.2478/auom-2025-0014ordered semigroupresiduated semigroupresiduated n-lattice08a7203g2503g1003c05 |
| spellingShingle | Zahiri Saeide Saeid Arsham Borumand On residuated n-lattice Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica ordered semigroup residuated semigroup residuated n-lattice 08a72 03g25 03g10 03c05 |
| title | On residuated n-lattice |
| title_full | On residuated n-lattice |
| title_fullStr | On residuated n-lattice |
| title_full_unstemmed | On residuated n-lattice |
| title_short | On residuated n-lattice |
| title_sort | on residuated n lattice |
| topic | ordered semigroup residuated semigroup residuated n-lattice 08a72 03g25 03g10 03c05 |
| url | https://doi.org/10.2478/auom-2025-0014 |
| work_keys_str_mv | AT zahirisaeide onresiduatednlattice AT saeidarshamborumand onresiduatednlattice |