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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A property for inverses in a partially ordered linear algebra
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by Taen Yu Dai and Ralph DeMarr
Trans. Amer. Math. Soc. 215 (1976), 285-292
DOI: https://doi.org/10.1090/S0002-9947-1976-0382116-2

Abstract:

We consider a Dedekind $\sigma$-complete partially ordered linear algebra A which has the following property: if $x \in A$ and $1 \leqslant x$, then $- u \leqslant {x^{ - 1}}$, where $u = {u^2}$. This property is used to show that A must be commutative. We also show that A is the direct sum of two algebras, each of which behaves like an algebra of real-valued functions.
References
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Bibliographic Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 215 (1976), 285-292
  • MSC: Primary 06A70
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0382116-2
  • MathSciNet review: 0382116