A proof of Weinberg's conjecture on latticeordered matrix algebras
Authors:
Jingjing Ma and Piotr J. Wojciechowski
Journal:
Proc. Amer. Math. Soc. 130 (2002), 28452851
MSC (2000):
Primary 06F25; Secondary 15A48
Published electronically:
March 15, 2002
MathSciNet review:
1908906
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
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 latticeordered algebra over in which the identity matrix 1 is positive, then is isomorphic to the latticeordered algebra with the usual lattice order. In particular, Weinberg's conjecture is true.
 1.
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, 1979. MR 82b:15013
 2.
G. Birkhoff and R. S. Pierce, Latticeordered rings, An. Acad. Brasil. Cienc. 28 (1956), 4169. MR 18:191d
 3.
P. Conrad, Latticeordered groups, Tulane Lecture Notes, Tulane University, 1970.
 4.
L. Fuchs, Partially ordered algebraic systems, Akademia Kiado, Budapest. MR 30:2090
 5.
J. Ma, Latticeordered matrix algebras with the usual lattice order, J. of Algebra 228 (2000), 406416. MR 2001d:16066
 6.
S. A. Steinberg, Finitelyvalued fmodules, Pacific J. Math. 40 (1972), 723737. MR 46:5205
 7.
S. A. Steinberg, On the scarcity of latticeordered matrix algebras II, Proc. Amer. Math. Soc. 128 (2000), no. 6, 16051612. MR 2000j:06011
 8.
E. C. Weinberg, On the scarcity of latticeordered matrix rings, Pacific J. Math. 19 (1966), 561571. MR 34:2635
 1.
 A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, 1979. MR 82b:15013
 2.
 G. Birkhoff and R. S. Pierce, Latticeordered rings, An. Acad. Brasil. Cienc. 28 (1956), 4169. MR 18:191d
 3.
 P. Conrad, Latticeordered groups, Tulane Lecture Notes, Tulane University, 1970.
 4.
 L. Fuchs, Partially ordered algebraic systems, Akademia Kiado, Budapest. MR 30:2090
 5.
 J. Ma, Latticeordered matrix algebras with the usual lattice order, J. of Algebra 228 (2000), 406416. MR 2001d:16066
 6.
 S. A. Steinberg, Finitelyvalued fmodules, Pacific J. Math. 40 (1972), 723737. MR 46:5205
 7.
 S. A. Steinberg, On the scarcity of latticeordered matrix algebras II, Proc. Amer. Math. Soc. 128 (2000), no. 6, 16051612. MR 2000j:06011
 8.
 E. C. Weinberg, On the scarcity of latticeordered matrix rings, Pacific J. Math. 19 (1966), 561571. MR 34:2635
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (2000):
06F25,
15A48
Retrieve articles in all journals
with MSC (2000):
06F25,
15A48
Additional Information
Jingjing Ma
Affiliation:
Department of Mathematical Sciences, University of HoustonClear 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/S0002993902064080
PII:
S 00029939(02)064080
Keywords:
Latticeordered 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 “Latticeordered groups and frings" 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
