Some comments and examples on generation of (hyper-)archimedean ℓ -groups and f -rings

A. W. Hager[1]; D. G. Johnson[2]

  • [1] Department of Mathematics Wesleyan University Middletown, CT, USA, 06459
  • [2] 5 W. Oak St. Ramsey, NJ 07446

Annales de la faculté des sciences de Toulouse Mathématiques (2010)

  • Volume: 19, Issue: S1, page 75-100
  • ISSN: 0240-2963

Abstract

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This paper systematizes some theory concerning the generation of ℓ -groups and reduced f -rings from substructures. We are particularly concerned with archimedean and hyperarchimedean groups and rings. We discuss the process of adjoining a weak order unit to an ℓ -group, or an identity to an f -ring and find significant contrasts between these cases. In ℓ -groups, hyperarchimedeanness and similar properties fail to pass from generating structures to the structures that they generate, as illustrated by a basic example of Conrad and Martinez which we revisit and elaborate. For reduced f -rings, on the other hand, these properties do inherit upwards.

How to cite

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Hager, A. W., and Johnson, D. G.. "Some comments and examples on generation of (hyper-)archimedean $\ell $-groups and $f$-rings." Annales de la faculté des sciences de Toulouse Mathématiques 19.S1 (2010): 75-100. <http://eudml.org/doc/115904>.

@article{Hager2010,
abstract = {This paper systematizes some theory concerning the generation of $\ell $-groups and reduced $f$-rings from substructures. We are particularly concerned with archimedean and hyperarchimedean groups and rings. We discuss the process of adjoining a weak order unit to an $\ell $-group, or an identity to an $f$-ring and find significant contrasts between these cases. In $\ell $-groups, hyperarchimedeanness and similar properties fail to pass from generating structures to the structures that they generate, as illustrated by a basic example of Conrad and Martinez which we revisit and elaborate. For reduced $f$-rings, on the other hand, these properties do inherit upwards.},
affiliation = {Department of Mathematics Wesleyan University Middletown, CT, USA, 06459; 5 W. Oak St. Ramsey, NJ 07446},
author = {Hager, A. W., Johnson, D. G.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {hyperarchimedean -groups; -rings; Archimedean -groups; weak order unit},
language = {eng},
month = {4},
number = {S1},
pages = {75-100},
publisher = {Université Paul Sabatier, Toulouse},
title = {Some comments and examples on generation of (hyper-)archimedean $\ell $-groups and $f$-rings},
url = {http://eudml.org/doc/115904},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Hager, A. W.
AU - Johnson, D. G.
TI - Some comments and examples on generation of (hyper-)archimedean $\ell $-groups and $f$-rings
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2010/4//
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - S1
SP - 75
EP - 100
AB - This paper systematizes some theory concerning the generation of $\ell $-groups and reduced $f$-rings from substructures. We are particularly concerned with archimedean and hyperarchimedean groups and rings. We discuss the process of adjoining a weak order unit to an $\ell $-group, or an identity to an $f$-ring and find significant contrasts between these cases. In $\ell $-groups, hyperarchimedeanness and similar properties fail to pass from generating structures to the structures that they generate, as illustrated by a basic example of Conrad and Martinez which we revisit and elaborate. For reduced $f$-rings, on the other hand, these properties do inherit upwards.
LA - eng
KW - hyperarchimedean -groups; -rings; Archimedean -groups; weak order unit
UR - http://eudml.org/doc/115904
ER -

References

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