Partial Order in Matrix Nearrings

Abstract Let N be a zero-symmetric (right) nearring with identity. We introduce partial order in the matrix corresponding to (defined by Pilz Near-rings: theory and its applications, North Holland, Amsterdam, 1983) . A positive cone is defined characterization theorem obtained. For convex ideal I , we prove that $${I^*}$$ I ∗ $$M_n(N)$$ M n ( N ) conversely, if then $${I_{*}}$$ Consequently, establish an order-preserving isomorphism between p.o. quotient nearrings $$M_n(N)/{I^*}$$ / $$M_n(N')/{(I')^*}$$ ′ where $$I'$$ are ideals of $$N'$$ respectively. Finally, some properties Archimedean ordering those nearrings.