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Multi-agent system has been known to provide distributed and collaborate problems solving environment. Each agent can work with itself knowledge base to improve the properties of reliability and real time of system. Currently the main description methods of agents are formalized languages, but the description capability of these languages about activity, interaction and evolution of agents is deficiency obviously. This paper abstracts the attributes and performance of agents by using algebra theory, puts forward the new concepts of innovation operation, cooperating operation and condition operation, and investigates properties and relations among them. It proves that the set of all agents of a multi-agent system and its innovation operation and condition operation form a semi-group respectively, the set and its cooperation form a commutative semi-group. The operation theory of agents proposed in this paper provides a new kind of method of agent description and established theoretic basis of more researches on agents and provides theoretic guidance for multi-agent system development.