Nonnegative solvability of linear equations in certain ordered rings
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- by Philip Scowcroft PDF
- Trans. Amer. Math. Soc. 358 (2006), 3535-3570 Request permission
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.References
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Additional Information
- Philip Scowcroft
- Affiliation: Department of Mathematics and Computer Science, Wesleyan University, Middletown, Connecticut 06459
- Email: pscowcroft@wesleyan.edu
- Received by editor(s): July 19, 2004
- Published electronically: March 1, 2006
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 358 (2006), 3535-3570
- MSC (2000): Primary 03C64; Secondary 06F20, 15A39
- DOI: https://doi.org/10.1090/S0002-9947-06-03978-X
- MathSciNet review: 2218988