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AbstractIn this paper we discuss the structural foundations of micro‐economic exchange. To treat various features of the exchange in a general form, we formulate an algebraic system to serve as an abstraction of a bookkeeping system. First, we introduce the concept of an algebraic system to describe the micro‐economic activities of economic units. Next, we formulate an axiomatic system to capture the essence of economic transactions. Finally, we explicate the bookkeeping system in terms of this axiomatic system and make clear various notions concerning the micro‐economic activities of economic units. In this paper we consider only basic properties of this algebraic system; these become the mathematical foundation for a theory of an economic system.