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
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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