Matrix Near-rings over Centralizer Near-rings

Abstract

For a finite group G and a subgroup A of Aut(G), let M A (G) denote the centralizer near-ring determined by A and G. The group G is an M A (G)-module. Using the action of M A (G) on G, one has the n × n generalized matrix near-ring Mat n (M A (G);G). The correspondence between the ideals of M A (G) and those of Mat n (M A (G);G) is investigated. It is shown that if every ideal of M A (G) is an annihilator ideal, then there is a bijection between the ideals of M A (G) and those of Mat n (M A (G);G).