On the scarcity of latticeordered matrix algebras II
Author:
Stuart A. Steinberg
Journal:
Proc. Amer. Math. Soc. 128 (2000), 16051612
MSC (1991):
Primary 06F25; Secondary 15A48
Published electronically:
September 23, 1999
MathSciNet review:
1641109
Fulltext PDF Free Access
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Abstract: We correct and complete Weinberg's classification of the latticeorders of the matrix ring and show that this classification holds for the matrix algebra where is any totally ordered field. In particular, the latticeorder of obtained by stipulating that a matrix is positive precisely when each of its entries is positive is, up to isomorphism, the only latticeorder of with . It is also shown, assuming a certain maximum condition, that is essentially the only latticeorder 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 436063390
Email:
ssteinb@uoft02.utoledo.edu
DOI:
http://dx.doi.org/10.1090/S0002993999051710
PII:
S 00029939(99)051710
Keywords:
Latticeordered 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
