Near-rings and near-ring groups with finiteness conditions

This work is delineating of various aspects of near-rings and near-ring groups dealing with annihilators of different types and finiteness conditions. The authors experience some broad-viewed aspects through such a structure with affluent potentialities for enriching the notions with rational extension of a categorical domain. Fascinating non-associative character of some algebraic structures creeps into the deliberations and thus reveals pleasant and striking flavor of this piece of asymmetric study of algebra. Goldie characters of such types of algebraic structures help one in dealing with many types of problems including singularity and non-singularity notions in broader aspects. The condition imposed on the singular subgroups circuitously helps one to see how so called rank function becomes a formative factor for proving the coincidence of the classical near-ring of quotients of a (right) near-ring with the complete one. Another deviated algebraic scrutiny is that near-rings as well as near-ring groups with partial ordering w.r.t. usual set inclusion lead us to multifaceted possible development for various types of structure theories in addition to some extensions.