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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A class of partially ordered linear algebras


Author: Ralph DeMarr
Journal: Proc. Amer. Math. Soc. 39 (1973), 255-260
MSC: Primary 06A70
MathSciNet review: 0313161
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Abstract: We consider a special type of partially ordered linear algebra which is like an algebra of real-valued functions. We show that various natural properties characterize this type of algebra. These natural properties relate the algebraic and order structures to each other.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0313161-3
PII: S 0002-9939(1973)0313161-3
Keywords: Dedekind $ \sigma $-complete partially ordered linear algebra, algebra of real-valued functions, matrix inequalities, $ f$-ring
Article copyright: © Copyright 1973 American Mathematical Society