Some examples of hyperarchimedean lattice-ordered groups

Anthony W. Hager, and Chawne M. Kimber. "Some examples of hyperarchimedean lattice-ordered groups." Fundamenta Mathematicae 182.2 (2004): 107-122. <http://eudml.org/doc/283254>.

@article{AnthonyW2004,
abstract = {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.},
author = {Anthony W. Hager, Chawne M. Kimber},
journal = {Fundamenta Mathematicae},
keywords = {hyperarchimedean lattice-ordered group; Yosida representation theorem; -extension},
language = {eng},
number = {2},
pages = {107-122},
title = {Some examples of hyperarchimedean lattice-ordered groups},
url = {http://eudml.org/doc/283254},
volume = {182},
year = {2004},
}

TY - JOUR
AU - Anthony W. Hager
AU - Chawne M. Kimber
TI - Some examples of hyperarchimedean lattice-ordered groups
JO - Fundamenta Mathematicae
PY - 2004
VL - 182
IS - 2
SP - 107
EP - 122
AB - 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.
LA - eng
KW - hyperarchimedean lattice-ordered group; Yosida representation theorem; -extension
UR - http://eudml.org/doc/283254
ER -