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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.


References [Enhancements On Off] (What's this?)

  • [1] Garrett Birkhoff, Lattice theory, Third edition. American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
  • [2] Taen-yu Dai, On some special classes of partially ordered linear algebras, J. Math. Anal. Appl. 40 (1972), 649–682. MR 0316342
  • [3] Ralph DeMarr, On partially ordering operator algebras, Canad. J. Math. 19 (1967), 636–643. MR 0212579
  • [4] Ralph DeMarr, A generalization of the Perron-Frobenius theorem, Duke Math. J. 37 (1970), 113–120. MR 0254592

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Additional Information

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