• 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 {Ni}, where each Ni 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.
Full Text:
pdfThis work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
© 2010-2022 International Journal of Mathematical Archive (IJMA) Copyright Agreement & Authorship Responsibility |