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

DOI:
https://doi.org/10.1090/S0002-9947-06-03978-X

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:
https://doi.org/10.1090/S0002-9947-06-03978-X

Received by editor(s):
July 19, 2004

Published electronically:
March 1, 2006

Article copyright:
© Copyright 2006
American Mathematical Society