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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Main Authors: Zahiri Saeide, Saeid Arsham Borumand
Format: Article
Language:English
Published: Sciendo 2025-03-01
Series:Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
Subjects:
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.
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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