On the Structure of a Class of Archimedean Lattice-Ordered Algebras

Authors

Melvin Henriksen, Harvey Mudd CollegeFollow
D. G. Johnson

Document Type

Article

Department

Mathematics (HMC)

Publication Date

1962

Abstract

By a Φ-algebra A, we mean an Archimedean lattice-ordered algebra over the real field R which has an identity element 1 that is a weak order unit. The Φ-algebras constitute the class of the title. It is shown that every ф-algebra is isomorphic to an algebra of continuous functions on a compact space X into the two-point compactification of the real line R, each of which is real-valued on an (open) everywhere dense subset of X. Under more restrictive assumptions on A, ropresentations of this sort have long been known. An (incomplete) history of them is given briefly in Section 2.

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,447.

Publisher pdf, posted with permission.

Rights Information

© 1962 Institute of Mathematics, Polish Academy of Sciences

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Recommended Citation

Henriksen, M., and D. G. Johnson. "On the structure of a class of archimedean lattice-ordered algebras." Fundamenta Mathematicae 50 (1962): 73-94.