Fields of quotients of lattice-ordered domains |
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| Authors: | Jingjing Ma R. H. Redfield |
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| Affiliation: | (1) Department of Mathematics, University of Houston-Clear Lake, 2700 Bay Area Boulevard, Houston TX 77058, USA;(2) Department of Mathematics, Hamilton College, 198 College Hill Road, Clinton, NY 13323, USA |
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| Abstract: | It is not known whether the field of fractions of an integral domain with a compatible lattice order has a compatible lattice order that extends the given order on the integral domain. The polynomial ring![$$mathbb{R}[x,x^{ - 1} ]$$](/content/91jb76hqn9v0d3dt/12_2004_Article_1875_TeX2GIFIEq1.gif) over the real numbers has a natural compatible lattice order, viz, the coordinatewise order  . We describe circumstances in which the field of fractions of![$$(mathbb{R}[x,x^{ - 1} ], + , cdot , geq )$$](/content/91jb76hqn9v0d3dt/12_2004_Article_1875_TeX2GIFIEq3.gif) has no archimedean lattice order that extends .Received May 2, 2003; accepted in final form June 4, 2004. |
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| Keywords: | 06F25 12E05 13B02 |
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