Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Reduction of systems of linear equations in ordinal variables
HTML articles powered by AMS MathViewer

by J. L. Hickman PDF
Proc. Amer. Math. Soc. 60 (1976), 265-269 Request permission

Abstract:

In this note we are concerned with a general finite system \begin{equation}\tag {$S$} \sum \limits _{i = 0}^{n - 1} {{x_i}{\alpha _{ji}} = {\beta _j};\quad j < m,}\end{equation} 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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 04A10
  • Retrieve articles in all journals with MSC: 04A10
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 265-269
  • MSC: Primary 04A10
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0419239-0
  • MathSciNet review: 0419239