On the scarcity

of lattice-ordered matrix algebras II

Author:
Stuart A. Steinberg

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1605-1612

MSC (1991):
Primary 06F25; Secondary 15A48

DOI:
https://doi.org/10.1090/S0002-9939-99-05171-0

Published electronically:
September 23, 1999

MathSciNet review:
1641109

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Abstract | References | Similar Articles | Additional Information

Abstract: We correct and complete Weinberg's classification of the lattice-orders of the matrix ring and show that this classification holds for the matrix algebra where is any totally ordered field. In particular, the lattice-order of obtained by stipulating that a matrix is positive precisely when each of its entries is positive is, up to isomorphism, the only lattice-order of with . It is also shown, assuming a certain maximum condition, that is essentially the only lattice-order of the algebra in which the identity element is positive.

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Additional Information

**Stuart A. Steinberg**

Affiliation:
Department of Mathematics, The University of Toledo, Toledo, Ohio 43606-3390

Email:
ssteinb@uoft02.utoledo.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-05171-0

Keywords:
Lattice-ordered algebra,
matrix algebra

Received by editor(s):
March 27, 1998

Received by editor(s) in revised form:
July 17, 1998

Published electronically:
September 23, 1999

Communicated by:
Ken Goodearl

Article copyright:
© Copyright 2000
American Mathematical Society