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A proof of Weinberg's conjecture on lattice-ordered matrix algebras

Authors:	Jingjing Ma Piotr J Wojciechowski

Institution:	Department of Mathematical Sciences, University of Houston-Clear Lake, 2700 Bay Area Boulevard, Houston, Texas 77058 ; Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, Texas 79968

Abstract:	Let $\mathbf{F}$ be a subfield of the field of real numbers and let $\mathbf{F}_{n}$ ( $n \geq 2$ ) be the $n \times n$ matrix algebra over $\mathbf{F}$ . It is shown that if $\mathbf{F}_{n}$ is a lattice-ordered algebra over $\mathbf{F}$ in which the identity matrix 1 is positive, then $\mathbf{F}_{n}$ is isomorphic to the lattice-ordered algebra $\mathbf{F}_{n}$ with the usual lattice order. In particular, Weinberg's conjecture is true.

Keywords:	Lattice-ordered algebra matrix algebra

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