Some examples of hyperarchimedean lattice-ordered groups

• Autorzy: Anthony W. Hager , Chawne M. Kimber
• Języki publikacji: EN

Abstrakty

EN

All ℓ-groups shall be abelian. An a-extension of an ℓ-group is an extension preserving the lattice of ideals; an ℓ-group with no proper a-extension is called a-closed. A hyperarchimedean ℓ-group is one for which each quotient is archimedean. This paper examines hyperarchimedean ℓ-groups with unit and their a-extensions by means of the Yosida representation, focussing on several previously open problems. Paul Conrad asked in 1965: If G is a-closed and M is an ideal, is G/M a-closed? And in 1972: If G is a hyperarchimedean sub-ℓ-group of a product of reals, is the f-ring which G generates also hyperarchimedean? Marlow Anderson and Conrad asked in 1978 (refining the first question above): If G is a-closed and M is a minimal prime, is G/M a-closed? If G is a-closed and hyperarchimedean and M is a prime, is G/M isomorphic to the reals? Here, we introduce some techniques of a-extension and construct a several parameter family of examples. Adjusting the parameters provides answers "No" to the questions above.

Kategorie tematyczne

• 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces
• 54C40: Algebraic properties of function spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 182
• Numer: 2
• Strony: 107-122

Daty

wydano

2004

Twórcy

autor

Anthony W. Hager

• Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT 06459, U.S.A.

autor

Chawne M. Kimber

• Department of Mathematics, Lafayette College, Easton, PA 18042, U.S.A.

Identyfikatory

DOI

10.4064/fm182-2-2