Maximal Homomorphism in Fundamental Theorem of Homomorphism Semiring

Abstract

Semiring is a generalization of ring. Some concepts in ring can be developed in semiring. The contructions of quotient semiring requires a specific ideal, namely Q-ideal. Different to the ring theory, the fundamental theorems of homomorphism on semiring needs a concept of maximal homomorphism, science the kernel of any maximal homomorphism is always Q-ideal.