On the structure of a class of archimedean lattice-ordered algebras

Abstract

. "On the structure of a class of archimedean lattice-ordered algebras." Fundamenta Mathematicae 50 (1962): 73-94.

The Space of Minimal Prime Ideals of a Commutative Ring

“…Let K be an algebraically closed field and A = K X K X K. In the ring KA of all K-valued functions on A, we denote We come now to the main result of the section. 3.4. Theorem.…”

“…Then ^=fl^ift(an). 3.10. Remarks, (i) As we mentioned in the first paragraph of §3, we do not know whether a ring without nonzero nilpotents whose space of minimal prime ideals is compact is necessarily an a.c. ring.…”

“…If jx"} is a sequence in the ring C(X) of all continuous real-valued functions on a topological space X (or, more generally, in a uniformly closed *-algebra in the sense of [3]), and x = X!n=i2""(|x"| Al), then J# (x) = H S3ixn). Proof.…”

“…This section is concerned with the special properties of the space of minimal prime ideals of a ring that happens to be the ring C(X) of all continuous real-valued functions on some completely regular space X. Most of the results apply equally well to *-algebras [3], that is, to archimedean lattice-ordered algebras over the reals with unity elements that are also weak order units. The 4>-algebras are definitely more general than subalgebras of algebras of the form C(X).…”

On α-regular archimedean f-rings

“…(b) Here is a formulation of the Henriksen-Johnson Representation Theorem; for the rest the reader is referred to [HJ61]:…”