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