Generalized Matrix Near Ring over Abstract Affine Near Ring

Near- rings and near -ring modules are the natural non-linear generalization of rings and ring modules. The first occurrence of near-rings was in 1905 when Dickson introduced near fields. Near -rings are very closely related to the theory of varieties of groups, and have applications in non-abelian homological algebra. The group -theoretic connection first appeared in work by H.Neumann 1954-1956. The theory of d.g near rings received a big boost when A.Frohlich published a series of papers in the period 1958-1962. In this book, we study some topics from near-ring such as abstract affine near rings, matrix near rings and generalized matrix near rings. In chapter three let A be an abstract affine near ring, N be a faithful near ring A-module and n be a positive integer. In this book we define the nn generalized matrixe near ring over A using the faithful near ring A-module N.