Lattice-Ordered Matrix Algebras with the Usual Lattice Order

✍ Scribed by Jingjing Ma

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 117 KB
• Volume: 228
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.8232

✦ Synopsis

Let R be a unital lattice-ordered algebra over a totally ordered field F and F n be the n × n n ≥ 2 matrix algebra over F. It is shown that under certain conditions R contains a lattice-ordered subalgebra which is isomorphic to (F n F + n . In particular, let (F n P) be a lattice-ordered algebra over F with the positive cone P. If a certain element is positive in F n P , then F n P is isomorphic to F n F + n .