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A proof of Weinberg's conjecture on lattice-ordered matrix algebras |
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| Authors: | Jingjing Ma Piotr J. Wojciechowski |
| Affiliation: | 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  be a subfield of the field of real numbers and let  ( ) be the  matrix algebra over  . It is shown that if  is a lattice-ordered algebra over  in which the identity matrix 1 is positive, then  is isomorphic to the lattice-ordered algebra  with the usual lattice order. In particular, Weinberg's conjecture is true. |
| Keywords: | Lattice-ordered algebra matrix algebra |
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