Some Studies On The Congruence Extension Properties Of Hamiltonian Semirings

In this thesis,we mainly study the congruence extension properties of two kinds of semirings.In particular,the congruences on Hamiltonian semirings and Hamiltonian ordered semirings are studied,the differences of congruence extension properties between two kinds of semirings are com?pared..We will divide the whole paper into three chapters.In chapter 1,we introduce the historical development background of semiring theory and its application value in the field of mathematics.Some related concepts to be used in this paper are also given.In chapter 2,we mainly study the congruence extension properties of Hamiltonian semirings.The definitions of Hamiltonian semirings and their related congruence extension properties are given,and the concrete Hamil-tonian semirings are given.Some examples of semirings having congruence extension properties are given.Finally,we give some properties of semirings with congruence extension property.In chapter 3,we study the congruence extension properties of Hamil-tonian ordered semirings and four kinds of congruence extension properties are discussed.Finally,we also discuss the differences between Hamiltonian semirings and Hamiltonian ordered semirings.