Prime Ideals in Group Near-rings

Abstract

The flow (or lack thereof) of several kinds of primeness between a zerosymmetric near-ring R and its group near-ring R[G] for certain groups G is discussed. In certain cases, results are contrasted against what happens in the matrix near-ring situation.2000 Mathematics Subject Classification: 16Y30

Group seminearrings

“…The elements of group nearring are generated by the function [r, g], where r ∈ S, g ∈ G, defined by ([r, g](µ))(h) = rµ(hg) for all µ ∈ S G , h ∈ G. Eventually, we define a group seminearring by using the similar approach used for defining group nearring by Le Riche et al [10]. Different types of ideals of grouprings are discussed in [5,6]. For group nearrings one can consult [5,6,10,11].…”

“…Different types of ideals of grouprings are discussed in [5,6]. For group nearrings one can consult [5,6,10,11].…”