Structural Derivations in Hilbert Algebras by Endomorphisms

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DOI: https://doi.org/10.28924/2291-8639-22-2024-213
Published: Nov 18, 2024
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Aiyared Iampan, Neelamegarajan Rajesh, C. Arivazhagi, R. Vennila, Structural Derivations in Hilbert Algebras by Endomorphisms, Int. J. Anal. Appl., 22 (2024), 213.

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Aiyared Iampan, Neelamegarajan Rajesh, C. Arivazhagi, R. Vennila

Abstract

This work introduces the concept of f-derivations in Hilbert algebras, exploring its theoretical foundation alongside a series of illustrative examples. We examine fundamental properties associated with f-derivations through rigorous analysis, shedding light on their algebraic structure and behaviour. In particular, we demonstrate that the kernel Kerdf(A) constitutes a near filter (subalgebra), while the fixed set Fixdf(f) forms a subalgebra within the Hilbert algebra A. These results provide new insights into the interaction between derivations and substructures in Hilbert algebras, offering potential avenues for further exploration in algebraic logic and related fields.

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