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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A proof of Weinberg’s conjecture on lattice-ordered matrix algebras
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by Jingjing Ma and Piotr J. Wojciechowski PDF
Proc. Amer. Math. Soc. 130 (2002), 2845-2851 Request permission

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
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 2845-2851
  • MSC (2000): Primary 06F25; Secondary 15A48
  • DOI: https://doi.org/10.1090/S0002-9939-02-06408-0
  • MathSciNet review: 1908906