Ordered Kernels of OBCI-Algebras in the Homomorphism Environment

Yang, Roh and Jun recently introduced kernels of homomorphisms in OBCI-algebras and left an ordered generalization of those kernels as a future work. As its answer, we introduce the concept of ordered kernels of OBCI-algebras in the homomorphism environment. To be more concrete, first of all, the notion of ordered kernels of OBCI-algebras is intruduced. Next, properties of those ordered kernels related to (ordered) subalgebras, (ordered) filters and functional compositions are discussed in homomorphisms of OBCI-algebras.