Endomorphisms and Their Role in Novel Derivations of Hilbert Algebras

Abstract

This study introduces and explores left--derivations, right--derivations, and -derivations of type  and type  within the framework of Hilbert algebras, focusing on their fundamental properties and structural significance. We show that the kernel of an -derivation, , forms a near filter and operates as a subalgebra of the Hilbert algebra . These findings enhance the understanding of Hilbert algebras and offer new perspectives on the role of derivations in algebraic logic.