# Some comments and examples on generation of (hyper-)archimedean $\ell $-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

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topHager, 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 -

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