Certain Hom-algebra Structure

This dissertation consists of five sections. We shall investigate the Hom-algebra. And we will gain some important propositions.The first and second sections are introduction and preliminaries respectively.In the third section, we introduce an equivalent condition of Hom-associative alge-bras. It is very useful to research frame of Hom-algebras. Then we spread the Hom-coassociativity condition. Next, we prove the isomorphic relationship (A(?)C*,μ(?)Δ*,η(?)ε*,α(?)β*)= (Homκ(C,A),*,η(?)ε,γ) when A or C is finite dimension. At last, we introduce the definition of Hom-antipode and gain some important propositions.In the forth section, we introduce the definition of weak-identity element. Then we investigate the braided Hom-bialgebra and get quantum Hom-Yang-Baxter equation.In the last section,we construct the Hom-weak bialgebra on the basis of the weak bialgebra. And we get some important propositions.