Ordered homomorphisms and kernels of ordered BCI-algebras

TL;DR

This paper extends the theory of ordered BCI-algebras by defining and analyzing ordered homomorphisms and kernels, exploring their properties and relationships with subalgebras, filters, and direct products.

Contribution

It introduces the concepts of ordered homomorphisms and kernels for ordered BCI-algebras and investigates their fundamental properties and structural implications.

Findings

Defined ordered homomorphisms and kernels.

Analyzed properties of subalgebras and filters.

Explored direct product structures.

Abstract

Recently Yang-Roh-Jun introduced the notion of ordered BCI-algebras as a generalization of BCI-algebras. They also introduced the notions of homomorphisms and kernels of ordered BCI-algebras and investigated related properties. Here we extend their investigation to ordered homomorphisms, i.e., order-preserving homomorphisms. To this end, the notions of ordered homomorphism and kernel of ordered BCI-algebras are first defined. Next, properties associated with (ordered) subalgebras, (ordered) filters and direct products of ordered BCI-algebras are addressed.