Lattice-Ordered Matrix Rings Over the Integers

REFERENCES

• Birkhoff , G. ( 1973 ). Lattice Theory . Amer. Math. Soc. Colloquium Pub. 25. Providence : Amer. Math. Soc .
   Google Scholar
• Birkhoff , G. , Pierce , R. S. ( 1956 ). Lattice-ordered rings . An. Acad. Brasil. Ci. 28 : 41 – 69 .
   Google Scholar
• Conrad , P. ( 1961 ). Some structure theorems for lattice-ordered groups . Trans. Amer. Math. Soc. 99 : 212 – 240 .
   Google Scholar
• Conrad , P. ( 1970 ). Lattice Ordered Groups . Tulane University .
   Google Scholar
• Darnel , M. ( 1995 ). Theory of Lattice-Ordered Groups . New York : Dekker .
   Google Scholar
• Dauns , J. ( 1994 ). Modules and Rings . Cambridge : Cambridge Univ. Press .
   Google Scholar
• Ma , J. , Wojciechowski , P. ( 2002a ). A proof of Weinberg's conjecture on lattice-ordered matrix algebras . Proc. Amer. Math. Soc. 130 : 2845 – 2851 .
   Web of Science ®Google Scholar
• Ma , J. , Wojciechowski , P. ( 2002b ). Lattice orders on matrix algebras . Algebra Univers. 47 : 435 – 441 .
   Web of Science ®Google Scholar
• Rotman , J. J. ( 2002 ). Advanced Modern Algebra . Pearson Education (Prentice Hall) , Upper Saddle River , NJ, USA .
   Google Scholar
• Steinberg , S. A. ( 2000 ). On the scarcity of lattice-ordered matrix algebras II . Proc. Amer. Math. Soc. 128 : 1605 – 1612 .
   Web of Science ®Google Scholar
• Weinberg , E. C. ( 1966 ). On the scarcity of lattice-ordered matrix rings . Pacific J. Math. 19 : 561 – 571 .
   Web of Science ®Google Scholar
• Communicated by I. Swanson.
   Google Scholar