Structure and Properties of Near Rings

The purpose of this paper is to formulate the properties and the structure of near-rings. The definition is the basis of this development. Since near-rings lack only the left distributive law and commutative addition to be rings, many of the properties of near-rings can be proven that are properties of rings. From the definition it can be seen that near- rings are groups under addition. Therefore, criteria can be developed to insure that multiplication is defined such that a near-ring is created. Some near-rings are exhibited, mostly from the theory already presented. Ideals of near-rings are also developed