Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Reduction of systems of linear equations in ordinal variables


Author: J. L. Hickman
Journal: Proc. Amer. Math. Soc. 60 (1976), 265-269
MSC: Primary 04A10
MathSciNet review: 0419239
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we are concerned with a general finite system

$\displaystyle \sum\limits_{i = 0}^{n - 1} {{x_i}{\alpha _{ji}} = {\beta _j};\quad j < m,}$ ($ S$)

of m linear equations in n variables, where the $ {\alpha _{ji}}$ and the $ {\beta _j}$ are positive ordinals, and the variables $ {x_i}$ range over ordinals.

In the particular case n = 1 we show that (S) can be reduced to a canonical form $ ({{\text{S}}^\ast})$ having solutions of a relatively simple type, and we use $ ({{\text{S}}^\ast})$ to obtain the solution-set of (S).

In the general case we show that (S) can be reduced to a finite sequence of single-variable systems, and again obtain the solution-set of (S) in terms of the solution-sets of these simpler systems.

We assume a knowledge of the elementary theory of ordinal arithmetic, such as may be found for example in [2].


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 04A10

Retrieve articles in all journals with MSC: 04A10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0419239-0
PII: S 0002-9939(1976)0419239-0
Article copyright: © Copyright 1976 American Mathematical Society