A property for inverses in a partially ordered linear algebra

Authors:
Taen Yu Dai and Ralph DeMarr

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

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a Dedekind -complete partially ordered linear algebra *A* which has the following property: if and , then , where . 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1976-0382116-2

Keywords:
Dedekind -complete partially ordered linear algebra,
algebra of real-valued functions,
*f*-ring,
matrix inequalities

Article copyright:
© Copyright 1976
American Mathematical Society