Fixed-Point Hoop Algebras and Lattice-Theoretic Properties of Derivation Classes

Ali Madanshekaf and Mohammad Mahdi Motamedi Nezhad

Journal of Mathematics, 2026, vol. 2026, 1-14

Abstract: We introduce three classes of derivations on hoop algebras—pseudo implicative, implicative, and f-implicative—and investigate their algebraic characteristics through detailed examples. We establish that, under natural conditions, the collection of pseudo implicative derivations forms a bounded distributive lattice. Further, we prove that the fixed-points sets of both implicative and f-implicative derivations inherit the structure of hoop algebras and, under additional constraints, form bounded distributive lattices. Finally, we show that the families of implicative and f-implicative derivations themselves constitute bounded distributive lattices under suitable assumptions.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4485821

DOI: 10.1155/jom/4485821

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