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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nonnegative solvability of linear equations in certain ordered rings


Author: Philip Scowcroft
Journal: Trans. Amer. Math. Soc. 358 (2006), 3535-3570
MSC (2000): Primary 03C64; Secondary 06F20, 15A39
Published electronically: March 1, 2006
MathSciNet review: 2218988
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Abstract: In the integers and in certain densely ordered rings that are not fields, projections of the solution set of finitely many homogeneous weak linear inequalities may be defined by finitely many congruence inequalities, where a congruence inequality combines a weak inequality with a system of congruences. These results extend well-known facts about systems of weak linear inequalities over ordered fields and imply corresponding analogues of Farkas' Lemma on nonnegative solvability of systems of linear equations.


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Additional Information

Philip Scowcroft
Affiliation: Department of Mathematics and Computer Science, Wesleyan University, Middletown, Connecticut 06459
Email: pscowcroft@wesleyan.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03978-X
PII: S 0002-9947(06)03978-X
Received by editor(s): July 19, 2004
Published electronically: March 1, 2006
Article copyright: © Copyright 2006 American Mathematical Society