Lattice-Ordered Matrix Algebras Over Real GCD-Domains

Abstract

Let R ⊂ ℝ be a GCD-domain. In this article, Weinberg's conjecture on the n × n matrix algebra M n (R) (n ≥ 2) is proved. Moreover, all the lattice orders (up to isomorphisms) on a full 2 × 2 matrix algebra over R are obtained.