Some comments and examples on generation of (hyper-)archimedean -groups and f-rings
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. S1, pp. 75-100.

This paper systematizes some theory concerning the generation of -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 -group, or an identity to an f-ring and find significant contrasts between these cases. In -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.

DOI : 10.5802/afst.1276
Hager, A. W. 1 ; Johnson, D. G. 2

1 Department of Mathematics Wesleyan University Middletown, CT, USA, 06459
2 5 W. Oak St. Ramsey, NJ 07446
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Hager, A. W.; 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, Série 6, Tome 19 (2010) no. S1, pp. 75-100. doi : 10.5802/afst.1276. http://archive.numdam.org/articles/10.5802/afst.1276/

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