Lattice-ordered 2×2 triangular matrix algebras

Lattice orders on 2 × 2 triangular matrix algebras

“…Let K be a totally ordered field and T 2 (K) the 2×2 upper triangular matrix algebra over K. In [2], it has been proved that there are four nonisomorphic lattice orders that make T 2 (K) into an -algebra over K in which the identity matrix is positive. The purpose of this article is to prove that lattice orders on T 2 (K) in which the identity matrix is not positive can, by the above method, be constructed from lattice orders in which the identity matrix is positive.…”

“…The purpose of this article is to prove that lattice orders on T 2 (K) in which the identity matrix is not positive can, by the above method, be constructed from lattice orders in which the identity matrix is positive. More precisely, any -algebra (T 2 (K), T 2 (K) ≥ ) is isomorphic or anti-isomorphic to an -algebra (T 2 (K), fP ), where P is the positive cone of one of those four lattice orders with the positive identity matrix given in [2], and f ∈ P is an J. Ma Algebra Univers.…”

“…In [2], it was shown that each lattice order on T 2 (K) in which 1 > 0 is isomorphic or anti-isomorphic to one of P 0 , P 1 , P 2 , P 3 . Clearly P 2 ⊆ P 1 ⊆ P 0 and they are all Archimedean lattice orders, but P 3 is non-Archimedean.…”

Lattice-ordered triangular matrix algebras

“…Then in [4], we have constructed all the lattice orders on 2 ×2 triangular matrix algebras over a totally ordered field to make them into latticeordered algebras ( -algebras) in which the identity matrix is positive. The present paper concerns how to characterize n × n triangular matrix -algebras with the entrywise lattice order for any n 2.…”