Meadows -- algebraic structures with three or more binary operations
The purpose of this paper is to explore algebraic structures with more than just two linked operations (binary operations). These are produced in the paper by simply adding further sequentially distributive operations to existing rings or fields; the resulting structures are termed meadows. A third operation can be added to a finite field, and occasionally a fourth. Section 1 gives the complete construction and classification of finite meadows. Section 2 presents some three-operation meadows over the integers and the rational numbers, and Section 3 describes a meadow with an infinite set of sequentially distributive operations, generated by ordinary addition and multiplication, over the real numbers. Section 4 demonstrates the essential uniqueness of the latter structure, and Section 5 contains some remarks concerning the significance of the new binary operations, including possible relations to bifurcation theory and chemical kinetics.
scientific article; zbMATH DE number 645080