Homomorphism theorems of ordered semirings

Abstract

In this paper, homomorphism theorems for ordered semirings are studied. We obtain some characterizations of the smallest compatible quasiorder or order-congruence generated by H. A homomorphism theorem and two isomorphism theorems of ordered semirings based on compatible quasiorders and order-congruences have been given. Finally, we have a characterization for the direct product of ordered semirings by using compatible quasiorders on an ordered semiring.