| A method is developed to make the ring of 2 x 2 triangular matrices of rational numbers into an Archimedean lattice-ordered ring with positive identity matrix. A detailed algorithm and implementation in the Mathematica RTM computer language are presented. By application of the algorithm, three different (up to isomorphism or anti-isomorphism) such lattice orderings are found, and the characterizations of the three lattice orderings are given. |
