Near-Rings and Near-Fields

The fundamental facts, the structure, and some applications of near-rings and near-fields are discussed. After the fundamental definitions and examples of near-rings, near-fields are discussed, as well as their relations to group theory and to geometry. Then the structure of near-rings (semisimplicity, simplicity, primitivity) is described, and the famous density theorem is presented, along with some applications to interpolation theory. Connections to universal algebra, to the design of statistical experiments, to geometry, to group theory, and to automata theory are discussed. Finally, the relations to dynamical systems and to graph theory are mentioned.