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Full-Text Articles in Physical Sciences and Mathematics
On The Structure Of A Class Of Archimedean Lattice-Ordered Algebras, Melvin Henriksen, D. G. Johnson
On The Structure Of A Class Of Archimedean Lattice-Ordered Algebras, Melvin Henriksen, D. G. Johnson
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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 …
Lattice-Ordered Rings And Function Rings, Melvin Henriksen, John R. Isbell
Lattice-Ordered Rings And Function Rings, Melvin Henriksen, John R. Isbell
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This paper treats the structure of those lattice-ordered rings which are subdirect sums of totally ordered rings -- the f-rings of Birkhoff and Pierce [4]. Broadly, it splits into two parts, concerned respectively with identical equations and with ideal structure; but there is an important overlap at the beginning.