A class of partially ordered linear algebras

Author:
Ralph DeMarr

Journal:
Proc. Amer. Math. Soc. **39** (1973), 255-260

MSC:
Primary 06A70

DOI:
https://doi.org/10.1090/S0002-9939-1973-0313161-3

MathSciNet review:
0313161

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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]**G. Birkhoff,*Lattice theory*, Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R.I., 1967. MR**37**#2638. MR**0227053 (37:2638)****[2]**T. Dai,*On a special class of partially ordered linear algebras*, J. Math. Anal. Appl.**40**(1972), 649-682. MR**0316342 (47:4890)****[3]**R. E. DeMarr,*On partially ordering operator algebras*, Canad. J. Math.**19**(1967), 636-643. MR**0212579 (35:3450)****[4]**-,*A generalization of the Perron-Frobenius theorem*, Duke Math. J.**37**(1970), 113-120. MR**0254592 (40:7800)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
06A70

Retrieve articles in all journals with MSC: 06A70

Additional Information

DOI:
https://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