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.

**[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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DOI:
http://dx.doi.org/10.1090/S0002-9939-1973-0313161-3

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

Article copyright:
© Copyright 1973
American Mathematical Society