• A NOTE ON LEFT IDEALS IN ZERO-SYMMETRIC BOOLEAN NEAR-RINGS

Abstract

In this note we prove that in a zero-symmetric Boolean near-ring every left ideal is a two –sided ideal.  We also prove that if N is a zero-symmetric Boolean near-ring then for every e Î N, Ne is an ideal of N. As a consequence we prove that every zero-symmetric Boolean near-ring N is a subdirect  product of near-rings {N_i}, where each N_i is a  near-ring with trivial multiplication, that is  xy = x if  y ≠0 and xy = 0 if   y = 0, for all  x, yÎ N.  In addition some interesting results are also proved.