A Simple Method for Generating Discrete Multi-Component Integrable Hierarchy

For M×N spectral matrix, a kind of operation ʘ which satisfies combination law (aʘb)ʘc=aʘ(bʘc) is introduced. The discrete multi−component zero-curvature equation is deduced by using the new operation ʘ, and a simple method for constructing discrete multi-component integrable hierarchy is proposed. As its application, the multi-component Toda hierarchy and its two kinds of integrable couplings are worked out.