An introduction to the theory of Hom—Hilbert algebras

초록

The concept of (commutative, bounded) Hom-Hilbert algebras is introduced, and examples are provided to illustrate it. Fundamental properties of the (commutative and bounded) Hom-Hilbert algebra are investigated, and a method for deriving the generalized Hilbert algebra from the Hom-Hilbert algebra is presented, and vice versa. A process is given in which every commutative Hom-Hilbert algebras form a poset structure. The join-semilattice is induced based on the commutative Hom-Hilbert algebra, and the meet-semilattice is induced based on the bounded Hom-Hilbert algebra. The commutative residuated lattice based on the bounded commutative Hom-Hilbert algebra is constructed.

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