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Nonnegative solvability of linear equations in certain ordered rings

Author(s): Philip Scowcroft
Journal: Trans. Amer. Math. Soc. 358 (2006), 3535-3570.
MSC (2000): Primary 03C64; Secondary 06F20, 15A39
Posted: March 1, 2006
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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: 10.1090/S0002-9947-06-03978-X
PII: S 0002-9947(06)03978-X
Received by editor(s): July 19, 2004
Posted: March 1, 2006
Copyright of article: Copyright 2006, American Mathematical Society

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