Symmetric bi-derivations of residuated lattices

In this paper, we introduced the notion of symmetric bi-derivations on residuated lattices and investigated some related properties. Some relationships between symmetric bi-derivation and k -isotone, k -contractive and k -ideal symmetric bi-derivations are given. Also, we introduce the sets of k -fi...

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Bibliographic Details
Published in:Annali dell'Università di Ferrara. Sezione 7. Scienze matematiche 2024-06, Vol.70 (2), p.235-248
Main Authors: Zaoui, Mbarek, Gretete, Driss, El Abbassi, El Mustapha, Fahid, Brahim
Format: Article
Language:English
Subjects:
Algebraic Geometry
Analysis
Derivation
Geometry
History of Mathematical Sciences
Lattices
Mathematics
Mathematics and Statistics
Numerical Analysis
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Summary:In this paper, we introduced the notion of symmetric bi-derivations on residuated lattices and investigated some related properties. Some relationships between symmetric bi-derivation and k -isotone, k -contractive and k -ideal symmetric bi-derivations are given. Also, we introduce the sets of k -fixed points of a symmetric bi-derivation and its structure is studied. In particular, we show that the “family” of sets of k -fixed points forms a residuated lattice.
ISSN:0430-3202
1827-1510
DOI:10.1007/s11565-023-00468-3