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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Jingjing Ma and Piotr J. Wojciechowski
Journal: Proc. Amer. Math. Soc. 130 (2002), 2845-2851
MSC (2000): Primary 06F25; Secondary 15A48
Published electronically: March 15, 2002
MathSciNet review: 1908906
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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.


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Additional Information

Jingjing Ma
Affiliation: Department of Mathematical Sciences, University of Houston-Clear Lake, 2700 Bay Area Boulevard, Houston, Texas 77058
Email: ma@cl.uh.edu

Piotr J. Wojciechowski
Affiliation: Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, Texas 79968
Email: piotr@math.utep.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06408-0
PII: S 0002-9939(02)06408-0
Keywords: Lattice-ordered algebra, matrix algebra
Received by editor(s): March 20, 2001
Received by editor(s) in revised form: May 16, 2001
Published electronically: March 15, 2002
Additional Notes: The results in this paper were presented at the conference “Lattice-ordered groups and f-rings" at the University of Florida, March 2001.
Dedicated: Dedicated to Professor Melvin Henriksen on his 75th birthday
Communicated by: Lance W. Small
Article copyright: © Copyright 2002 American Mathematical Society