PARTIAL ORDER IN MODULE OVER A MATRIX NEARRING

Let M_n (N) be a matrix nearring over the nearring N with identity and let Nⁿ be the direct sum of n-copies of the group (N, +). We introduce a partial order in the M_n (N)-group Nⁿ corresponding to the partial order in N-group (over itself). We define a positive cone in M_n (N)-group Nⁿ and obtain its characterization. For a convex ideal of_N N, the corresponding ideal in M_n (N)-group Nⁿ is described; and conversely, if I is a convex ideal in M_n (N)-group Nⁿ, then the ideal I_∗∗ is convex in N (over itself). This establishes the one-one correspondence between the convex ideals of the p.o. N-group_N N and those of p.o. M_n (N)-group Nⁿ.